train speed problem solving

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Problems on Trains

Problems on Trains - Quantitative Aptitude for Government Exams

Train problems form an integral part of the time and speed questions which are frequently asked in the quantitative aptitude section of various Government exams . These questions are different from the basic speed, distance and time questions and require a different approach to be answered.

Mostly the number of questions asked from the train problems topic varies between 1-3 and are mostly asked in the word problems format.

Aspirants who wish to know the other topics which are a part of the quantitative aptitude section, along with the exams in which this section is included and sample questions, can visit the linked article.

With the increased competition and the level of exam, it is important that a candidate gives equal attention to the preparation of every single topic in order to ace the examination.

So, for candidates assistance, we have discussed in detail the concept of train-based problems, important formulas related to the same, tips to solve the questions easily and efficiently, along with some sample questions to prepare.

Aspirants are free to check the various other quantitative aptitudes related topics and articles given below:

Problems on Train – Basic Concept

Similar to the concept of speed, distance and time, train problems are specifically based on evaluating the speed, distance covered and time is taken by a train under different conditions.

The weightage of questions asked from this topic in the quantitative aptitude section of various Government exams is mostly between 1-3 marks and the common exams which include this topic in their syllabus are Bank, Insurance, SSC, RRB and other major Government exams.

There are specific formulas which are to be used to find answers to the train-based questions and candidates must memorise them in order to crack the answer for problems on trains.

Interested candidates can also check the 10 Simple Maths Shortcuts and Tricks to ace the quantitative aptitude section at the linked article.

Given below are the links with the detailed syllabus for various competitive exams for the reference of candidates:

Types of Questions on Train Problems

Over the years, the exam pattern has changed with the increase in the number of applicants and every year candidates notice a new pattern or format in which questions are asked for various topics in the syllabus.

It is important that a candidate is aware of the types in which a question may be framed or asked in the examination to avoid any risk of losing marks.

Thus, given below are the type of questions which may be asked from the train-based problems:

Time Taken by Train to Cross any stationary Body or Platform – Question may be asked where the candidate has to calculate the time taken by a train to cross a stationary body like a pole or a standing man or a platform/ bridge
Time Taken by 2 trains to cross each other – Another question that may be asked is the time two trains might take to cross each other
Train Problems based on Equations – Two cases may be given in the question and the candidates will have to form equations based on the condition given

Aspirants must also refer to the important pointer given below for the Train problems.

The image given below mentions the basic points a candidate must remember in order to answer the train based word problems:

Problems on Trains - Quantitative Aptitude for Government Exams

Important Formulas

To solve any numerical ability question a candidate needs to memorise the related formulas to be able to answer the questions easily and efficiently.

Given below are the important train-based questions formulas which shall help candidates answer the questions based on this topic:

Speed of the Train = Total distance covered by the train / Time taken
If the length of two trains is given, say a and b, and the trains are moving in opposite directions with speeds of x and y respectively, then the time taken by trains to cross each other = {(a+b) / (x+y)}
If the length of two trains is given, say a and b, and they are moving in the same direction , with speeds x and y respectively, then the time is taken to cross each other = {(a+b) / (x-y)}
When the starting time of two trains is the same from x and y towards each other and after crossing each other, they took t1 and t2 time in reaching y and x respectively, then the ratio between the speed of two trains = √t2 : √t1
If two trains leave x and y stations at time t1 and t2 respectively and travel with speed L and M respectively, then distanced from x, where two trains meet is = (t2 – t1) × {(product of speed) / (difference in speed)}
The average speed of a train without any stoppage is x, and with the stoppage, it covers the same distance at an average speed of y, then Rest Time per hour = (Difference in average speed) / (Speed without stoppage)
If two trains of equal lengths and different speeds take t1 and t2 time to cross a pole, then the time taken by them to cross each other if the train is moving in opposite direction = (2×t1×t2) / (t2+t1)
If two trains of equal lengths and different speeds take t1 and t2 time to cross a pole, then the time taken by them to cross each other if the train is moving in the same direction = (2×t1×t2) / (t2-t1)

Other related links to prepare for Government exams have been given below for your reference:

Tips and Tricks to Solve Train Problems

To assist aspirants to prepare for and ace the quantitative aptitude section, given below are a few tips which may help you answer the train problems quicker and more efficiently:

Always read the question carefully and do not haste in answering it as the train-based questions are usually presented in a complex manner
Once you read the question, try to apply a formula in them, this will may solution direct and save you some time
Do not guess if you are not sure. Since there is negative marking in competitive exams, ensure that you do not make assumptions and answer the questions
Do not over complicate the question and spend too much time on solving it if you are not able to answer
In case of confusion, you can also refer to the options given in the objective type papers and try finding the answer with the help of options given

Candidates can refer to the below-mentioned links and solve more and more mock tests, question papers and practise papers to apprehend the level of the exam better:

Free Online Government Exam Quiz
Bank PO Question Papers
Free Online Mock Test Series with Solutions
Previous Year Question Papers PDF with Solutions

Problems on Train – Sample Questions

Try solving the sample questions given below based on Train problems and practise more to score more in the upcoming Government exams.

Q 1. A train running at the speed of 56 km/hr crosses a pole in 18 seconds. What is the length of the train?

Answer: (4) 280m

Speed = {56 × (5/18)} m/sec = (140/9) m/sec

Length of the train (Distance) = Speed × Time = {(140/9) × 18} = 280 m

Q 2. Time is taken by two trains running in opposite directions to cross a man standing on the platform in 28 seconds and 18 seconds respectively. It took 26 seconds for the trains to cross each other. What is the ratio of their speeds?

Answer: (5) 4:1

Let the speed one train be x and the speed of the second train be y

Length of the first train = Speed × Time = 28x

Length of second train = Speed × Time = 18y

So, {(28x+18y) / (x+y)} = 26

⇒ 28x+18y = 26x+26y

Therefore, x:y = 4:1

Q 3. It takes a 360 m long train 12 seconds to pass a pole. How long will it take to pass a platform 900 m long?

Answer: (3) 42 seconds

Speed = (360/12) m/sec = 30 m/sec

Required Time = {(360+900) / 30} = 1260 / 30 = 42 seconds

Q 4. A train 300 m long is running at a speed of 54 km/hr. In what time will it pass a bridge 150 m long?

Answer: (2) 30 seconds

Speed = {54 × (5/18)} m/sec = 15 m/sec

Total distance which needs to be covered = (300+150)m = 450m

Time = Distance/Speed

Required Time = 450 / 15 = 30 seconds

Candidates must also practise more questions to understand the topic even better and to be able to answer any question from this topic if asked in the final examination.

Given below are a few other preparation links for your assistance:

For any further details regarding the competitive exams, candidates can turn to BYJU’S and get the study material or preparation tips.

Government Exams Related Links

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Speed of Train

Speed of train will help us to calculate different types of problems on motion.

1. When a train passes a stationary object:

Let x be the length of the train which includes the engine also. When the end of the train passes the object, then the engine of the train has to move a distance equal to the train.

Then the time taken by the train to pass the stationary object = length of the train/speed of the train

2. When a train passes a stationary object having some length:

When the end of the train passes the stationary object having some length, then the engine of the train has to move a distance equal to the sum of the length of the train and stationary object.

Then the time taken by the train to pass the stationary object = (length of the train + length of the stationary object)/speed of the train

Problems to calculate the motion or speed of train:

1. Find the time taken by a train 150 m long, running at a speed of 90 km/hr in crossing the pole.

Solution:

Length of the train = 150m

Speed of the train = 90 km/hr

= 90 × 5/18 m/sec

= 25m/sec

Therefore, time taken by the train to cross the pole = 150 m/25m/sec = 6 seconds.

2. A train 340 m long is running at a speed of 45 km/hr. what time will it take to cross a 160 m long tunnel?

Length of the train = 340 m

Length of the tunnel = 160m

Therefore, length of the train + length of the tunnel = (340 + 160) m = 500m

Speed of the train = 45 km/hr

Speed of the train = 45 × 5/18 m/sec

= 25/2 m/sec

= 12.5 m/sec

Therefore, time taken by the train to cross the tunnel = 500 m/12.5 m/sec.

= 40 seconds.

3. A train is running at a speed of 90 km/hr. if it crosses a pole in just 10 second, what is the length of the train?

Speed of the train = 90 × 5/18 m/sec = 25 m/sec

Time taken by the train to cross the pole = 10 seconds

Therefore, length of the train = 25 m/sec × 10 sec = 250 m

4. A train 280 m long crosses the bridge 170 m in 22.5 seconds. Find the speed of the train in km/hr

Length of the train = 280 m

Length of the bridge = 170 m

Therefore, length of the train + length of the bridge = 280 m + 170 m = 450 m

Time taken by the train to cross the bridge = 22.5 sec = 45/2 sec.

Therefore, speed of train = 450 m/22.5 m/sec = 450/45/2 m/sec = 20 m/sec

To convert the speed from m/sec to km/hr, multiply by 18/5

Therefore, speed of the train = 20 × 18/5 km/hr = 72 km/hr

Relationship between Speed, Distance and Time

Conversion of Units of Speed

Problems on Calculating Speed

Problems on Calculating Distance

Problems on Calculating Time

Two Objects Move in Same Direction

Two Objects Move in Opposite Direction

Train Passes a Moving Object in the Same Direction

Train Passes a Moving Object in the Opposite Direction

Train Passes through a Pole

Train Passes through a Bridge

Two Trains Passes in the Same Direction

Two Trains Passes in the Opposite Direction

8th Grade Math Practice From Speed of Train to HOME PAGE

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Algebra: Speed and Distance Problems

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Have you ever heard of a word problem like this one? "Train A heads north at an average speed of 95 miles per hour, leaving its station at the precise moment as another train, Train B, departs a different station, heading south at an average speed of 110 miles per hour. If these trains are inadvertently placed on the same track and start exactly 1,300 miles apart, how long until they collide?"

If that problem sounds familiar, it's probably because you watch a lot of television (like me). Whenever TV shows talk about math, it's usually in the context of a main character trying but failing miserably to solve the classic "impossible train problem." I have no idea why that is, but time and time again, this problem is singled out as the reason people hate math so much.

Kelley's Cautions

Make sure that the units match in a travel problem. For instance, if the problem says you traveled at 70 miles per hour for 15 minutes , then r = 70 and t = 0.25. Since the speed is given in miles per hour , the time should be in hours also, and 15 minutes is equal to .25 hours. I got that decimal by dividing 15 minutes by the number of minutes in an hour: 15 60 = 1 4 = 0.25.

In fact, it's not so hard. This, like any distance and rate of travel problem, only requires one simple formula:

Distance traveled ( D ) is equal to your rate of speed ( r ) multiplied by the time ( t ) you traveled that speed. What makes most distance and rate problems tricky is that you usually have two things traveling at once, so you need to use the formula twice at the same time. In this problem, you'll use it once for Train A and once for Train B.

To keep things straight in your mind, you should use little descriptive subscripts. For example, use the formula D A = r A · t A for Train A's distance, speed, and time values and use the formula D B = r B · t B for Train B.

Critical Point

The little A 's in the formula D A = r A · t A don't affect the values D, r , and t . They're just little labels to ensure that you only plug values corresponding to Train A into that formula.

Example 4 : Train A heads north at an average speed of 95 miles per hour, leaving its station at the precise moment as another train, Train B, departs a different station, heading south at an average speed of 110 miles per hour. If these trains are inadvertently placed on the same track and start exactly 1,300 miles apart, how long until they collide?

Solution : Two trains means two distance formulas: D A = r A · t A and D B = r B · t B . Your first goal is to plug in any values you can determine from the problem. Since Train A travels 95 mph, r A = 95; similarly, r B = 110.

Notice that the problem also says that the trains leave at the same time. This means that their travel times match exactly. Therefore, instead of denoting their travel times as t A and t B (which suggests they are different), I will write them both as t (which suggests they are equal). At this point, your formulas look like this:

= 95

= 110

Even though you added the distances in this problem, you won't always do soit depends on how the problem is worded. In Problem 3, for example, you will not calculate a sum.

Here's the tricky step. The trains are heading toward one another on a track that's 1,300 miles long. Therefore, they must collide when, together, both trains have traveled a total of 1,300 miles. Of course, Train B is going to travel more of those 1,300 miles than Train A, since it's traveling faster, but that doesn't matter. You don't even have to figure out how far each train will go. All that matters is that when D A + D B = 1300, it's curtains. Luckily, you happen to know what D A and D B are (95 t and 110 t , respectively) so plug those into the equation and solve.

You've Got Problems

Problem 3: Dave rode his bike from home to a 7-11 at an average speed of 17 mph, and the trip took 1.25 hours. However, as he pulled up to the store, he rode over some glass, causing both tires to go flat. Because of this rotten luck, he had to push his bike back home at an average speed of 3 mph. How long did the trip home take?

D A + D B = 1300
95 t + 110 t = 1300
205 t = 1300
t 6.341 hours

So, the trains will collide in approximately 6.341 hours.

Excerpted from The Complete Idiot's Guide to Algebra © 2004 by W. Michael Kelley. All rights reserved including the right of reproduction in whole or in part in any form. Used by arrangement with Alpha Books , a member of Penguin Group (USA) Inc.

You can purchase this book at Amazon.com and Barnes & Noble .

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Problems on Trains – Concept, Formulas and Practice Questions

Problems on trains: concept.

Problems on Trains, like concepts of speed, distance, and time, focus on evaluating a train’s speed, distance traveled, and time spent under various conditions.

The weightage of questions asked from this topic in the quantitative aptitude component of various government exams frequently ranges between 1 or 2 marks, and the most common exams that contain this topic in its syllabus include Bank, Insurance, SSC, RRB, and other important government exams.

Important formulas

formulas
The train’s speed is calculated as	$$ \frac{the \ total \ distance \ reached}{divided \ by \ the \ time \ taken} $$
If the length of two trains is specified, say a and b, and the trains are moving in opposite directions with speeds of x and y, then the time taken for trains to cross each other	$$\frac{(a+b)}{(x+y)}$$
If the length of two trains is specified, say a and b, and they are moving in the same direction, with speeds x and y consequently, the time taken to cross each other is	$$\frac{(a+b)}{(x-y)}$$
When the starting time of two trains is the same from x and y towards each other, and after crossing each other, they needed t and t time to reach y and x respectively, then the ratio between the speed of two trains	$$ √t2: √t1 $$
If two trains leave x and y stations at times t and t , respectively, and travel at speeds L and M, then the distance from x where two trains meet is	$$ = (t2 – t1) × \frac {product \ of \ speed}{difference\ in \ speed} $$
If a train’s average speed without a stoppage is x and it covers the same distance with a stoppage at an average speed of y, then the rest time per hour	$$ = \frac {difference\ in \ average\ speed}{speed \ without \ stoppage}$$
If two trains of equal lengths and different speeds take t and t time to pass a pole, then the time taken for them to cross each other if they are running in opposing directions	$$ = \frac{2×t1×t2}{t2+t1}$$
If two trains of equal lengths and different speeds take t1 and t2 time to cross a pole, then the time taken for them to cross each other if they are heading in the same direction	$$ =\frac{2×t1×t2}{t2-t1} $$

Tips & Tricks for Solving Train Problems

To help hopefuls prepare for and conquer the quantitative aptitude section, here are a few pointers that will help you solve train problems faster and more efficiently:

Always read the question carefully and do not hasten to answer it, as train-based questions are frequently given in a complex manner.
After reading the questions, try to apply a formula to them; this may result in a direct solution and save you time.
Don’t guess if you’re not sure. Since there is negative marking in competitive exams, make sure you don’t make assumptions and answer the questions.
If you are unable to answer, do not overcomplicate the question or devote too much effort to solving it.
In case of confusion, you can also refer to the options supplied in the objective type papers and try to discover the answer using the options given.

Practice Quizzes

– Coming Soon

Sample Questions: Problems on Trains

Q1. A train takes 90 seconds to cross a poll with speed of 60 km/h. Find the length of the train?

a) 1500 m b) 1250 m c) 1350 m d) 1400 m

Answer: (A) Speed of train = 60 km/h × 5/18 × 90 =1500m

Q2. A train crosses a pole in 15 sec and a 100 m long platform in 25 sec, what is the length of the train?

a) 90 m b) 120 m c) 150 m d) 180 m

Answer: C Let the speed of train be x m/s Length of the train = 15×x = 15x Train crosses 100 m long platform in 25 sec Total length which the train is covering (15x + 100) m Time taken = 25 sec 15x + 100 = 25 × x 100 = 10x 10 m/s = x Length of the train = 10 × 15 = 150 m

Q3. How many poles a train crosses when travelling with a speed of 45 kmph in 4 hour. If the distance between two poles is 50 m and poles are counting from starting.

a) 1001 b) 3601 c) 3000 d) 1801

Answer: B Distance = Speed × Time = 180 × 1000 = 180000 No. of poles = 180000/50 = 3600

Q4. A train travel with a speed of 7 kmph and another train travel with a speed of 14 kmph. If they cross each other then find the average speed.

a) 17/3 kmph b) 28/3 kmph c) 29/3 kmph d) 19/3 kmph

Answer: B Average Speed = (2 × 7 × 14)/ (7 + 14) = 196/21 = 28/3 kmph

Q5. A train starts from station A at the speed of 50 km/hr and another train starts from station B after 30 min at the speed of 150 km/hr towards each other. Find the distance of their meeting point from Station A. The distance between A and B is 725 km.

a) 200 km b) 250 km c) 225 km d) None of these

Answer: A Distance travelled by first train in ½ hour = 50 × ½ = 25 km Remaining distance = 725 – 25 = 700 Time = 700/(150+50) = 3.5 hour Relative speed = 150 + 50 = 200 kmph Distance travelled by first train in (3.5+0.5) hour = 50 × 4 = 200 km

Q6. Train A of length 250 m crosses a pole in 25 seconds. Train B travelling at the same speed crosses a 400 m long platform in 1 minute. Find the time taken by train B to cross train A, if the train A is stationary.

a) 45 seconds b) 42 seconds c) 40 seconds d) 48 seconds

Answer: A Speed of train A = 250/25 = 10 m/sec So, speed of train B = 10 m/sec Let the le o B ‘x’ . Then, (x + 400)/10 = 60 x = 200 m Total length of both trains = (250 + 200) = 450 m So, time taken by train B to cross train A = 450/10 = 45 seconds.

Q7. At starting 1/3rd of passenger left and 96 passengers boarding the train, again 1/2 of passenger left and 12 passengers boarding the train now there are total 248 passengers are in the train. Find how many passengers are there at starting?

a) 865 b) 664 c) 564 d) 789

Answer: C According to the question, 248 – 12 = 236 1/2 of passenger left the train it means passenger = 2 ×236 = 472 If 96 passengers already board the train then = 472 – 96 =376 1/3 rd of passenger left the train it means 2/3x = 376 x = 188 × 3 = 564 So, initially there are total 564 passengers.

Q8. The Length of train A is 200 m and length of train B is 400 m. They travel in same direction they will take 30 sec and they travel in opposite direction they will take 6 sec to reach the destination. Find the total speed of the train.

a) 6000 km/hr b) 3000 km/hr c) 7200 km/hr d) 3600 km/hr

Answer: D Speed = Distance/time (s1 + s2)/ (s1 – s2) = 5/1 s1/ s2 = 3/2 When train travel in opposite direction, 600 = 5x × 6 600 = 30x x = 600/30 x = 20 Total speed = 5x = 5 × 20 = 100 m/sec = 1000 × 18/5 = 3600 km/hr

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Frequently Asked Questions About Problems on Trains

Q1. What is the definition of a train problem? Problems on Trains: Concept, Tips, Tricks, and Examples Train Problems – A Basic Concept. Train problems, like the notion of speed, distance, and time, are centered on evaluating a train’s speed, distance traveled, and time spent under various conditions.

Q2. What is the formula for speed and time train problems? The formula t = d/s indicates that time equals distance divided by speed, which ultimately yields the time measured in train problems. Ans. To find the speed in train problems, use the formula speed = distance divided by time.

Q3. What is the most important formula for a train? Remember some important formulas for train problems to get quick solutions. x km/hr = x*(5/18) m/s, but x m/s equals x*(18/5) km/hr. The time it takes for a train of length/meters to pass a pole, a single post, or a standing man is equivalent to the time it takes to cover/meters.

Browse more Topics under Time And Speed

Distance/Speed Relation
Data Sufficiency
Relative Speed and Conversions
Time & Speed Practice Questions

Solved Examples

Example 2: A certain train is 125 m long. It passes a man, running at 5 km/hr in the same direction in which the train is going. It takes the train 10 seconds to cross the man completely. Then the speed of the train is:

A) 60 km/h B) 66 km/h C) 50 km/h D) 55 km/h

Answer: Here we will have to use the concept of the relative speed. The relative speed of two objects is the sum of their individual speeds if they are moving opposite to each other. If the two objects are moving in the same direction, then their relative speed is equal to the difference between the two speeds. Hence if the man was at rest or we can with respect to the man = ( 125/10 )m/sec Therefore, this speed of the train = ( 25/2 )m/sec. In other words we can write, this speed = ( (25/2) × (18/5) ) km/hr = 45 km/hr.

Now, let the speed of the train be = x km/hr. Then, the relative speed of the train with respect to the man = (x – 5) km/hr. Therefore, we must have, (x – 5) = 45 or x = 50 km/hr. Therefore, the correct option is C) 50 km/h.

Example 3: Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds. The ratio of their speeds is:

A) 2: 3 B) 3:2 C) 1:3 D) 3:1

Answer: Let the speeds of the two trains be = x m/s and y m/s respectively. Then, the length of the first train = 27x meters, and length of the second train = 17y meters.

We can write: ( 27x + 17y ) / (x+ y )= 23 Or 27x + 17y = 23x + 23y, therefore we have: 4x = 6y and ( x/y ) = ( 3/2 ). Hence the correct option here is B) 3:2

Example 4: A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?

A) 20 s B) 30 s C) 40 s D) 50 s

Answer: We have already seen the formula for converting from km/hr to m/s: x km/hr =[ x × ( 5/18) ]m/s.

Therefore, Speed =[45 x (5/18) m/sec = (25/2)m/sec.

Thus the total distance to be covered = (360 + 140) m = 500 m. Also, we know that the formula for finding Time = ( Distance/Speed ) Hence, the required time = [ (500 x 2)/25 ] sec = 40 sec.

Practice Questions

Q 1: A jogger running at 9 km/h alongside a railway track in 240 meters ahead of the engine of a 120 meters long train running at 45 km/h in the same direction. In how much time will the train pass the jogger?

A) 66 s B) 72 s C) 63 s D) 36 s

Ans: D) 36 s

Q 2: Two trains are moving in opposite directions at a speed of 60 km/hr and 90 km/hr respectively. Their lengths are 1.10 km and 0.9 km respectively. The time taken by the slower train to cross the faster train in seconds is:

A) 44 s B) 48 s C) 52 s D) 200 s

Ans: B) 48 s

Q 3: Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 seconds. The length of each train is:

A) 25 m B) 50 m C) 75 m D) 100 m

Ans: B) 50 m

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Time & Speed

Data Sufficiency – Time And Speed
Relative Speed And Conversions

6 responses to “Distance/Speed Relation”

How can u solve ex 4

Many of your questions are wrong let alone solutions. These waste our precious time and cause confusion

The answer for Example 4 is wrong. The correct answer 425.6.

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PROBLEMS ON TRAINS WITH SOLUTIONS

1. To convert the speed km per hour to meter per speed, multiply 5/18.

2. To convert the speed meter per second to km per hour, multiply 5/18.

3. Let the length of the train be L meters.

Distance traveled to pass a standing man = L meters

Distance traveled to pass a pole = L meters

4. Let the length of the train be 'a' meters and the length of the platform be 'b' meters.

Distance traveled to pass the platform is (a + b) meters

5. If two trains are moving on the same directions with speed of 'p' m/sec and 'q' m/sec (here p > q), then their relative speed is

= (p - q) m/sec

6. If two trains are moving opposite to each other in different tracks with speeds of 'p' m/sec and 'q' m/sec, then their relative speed is

= (p + q) m/sec

7. Let 'a' and 'b' are the lengths of the two trains.

They are traveling on the same direction with the speed 'p' m/sec and 'q' m/sec (here p > q), then the time taken by the faster train to cross the slower train

= (a + b)/(p - q) seconds

8. Let 'a' and 'b' are the lengths of the two trains.

They are traveling opposite to each other in different tracks with the speed 'p' m/sec and 'q' m/sec, then the time taken by the trains to cross each other

= (a + b)/(p + q) seconds

9. Two trains leave at the same time from the stations P and Q and moving towards each other.

After crossing, they take 'p' hours and 'q' hours to reach Q and P respectively.

Then the ratio of the speeds of two t rains is √q : √p.

10. Two trains are running in the same direction/opposite direction.

The person in the faster train observes that he crosses the slower train in 'm' seconds.

Then the distance covered in 'm' seconds in the relative speed is

= length of the slower train

11. Two trains are running in the same direction/opposite direction.

The person in the slower train observes that the faster train crossed him 'm' seconds.

= length of the faster train

Problem 1 :

If the speed of a train is 20 m/sec, find the speed the train in km/hr.

speed = 20 m/sec

To convert m/sec to km/h, multiply the given m/sec by 18/5.

= 20 x 18/5 km/hr

Problem 2 :

The length of a train is 300 meter and length of the platform is 500 meter. If the speed of the train is 20 m/sec, find the time taken by the train to cross the platform.

Distances needs to be covered to cross the platform is

= sum of the lengths of the train and platform

= 300 + 500

= 800 meters

Time taken to cross the platform is

= distance/speed

= 40 seconds

Problem 3 :

A train is running at a speed of 20 m/sec. If it crosses a pole in 30 seconds, find the length of the train in meters.

The distance covered by the train to cross the pole is

= length of the train

Given : Speed is 20 m/sec and time taken to cross the pole is 30 seconds.

distance = speed ⋅ time

length of the train = speed ⋅ time

= 20 ⋅ 30

= 600 meters

Problem 4 :

It takes 20 seconds for a train running at 54 km/h to cross a platform. And it takes 12 seconds for the same train in the same speed to cross a man walking at the rate of 6 km/h in the same direction in which the train is running. What is the length of the train and length of platform (in meters).

Relative speed of the train to man = 54 - 6 = 48 km/hr.

= 48 ⋅ 5/18 m/sec

= 40/3 m/sec

When the train passes the man, it covers the distance which is equal to its own length in the above relative speed.

Given : It takes 12 seconds for the train to cross the man So, the length of the train = relative speed x time

= (40/3) ⋅ 12

Speed of the train = 54 km/h

= 54 ⋅ 5/18 m/sec

When the train crosses the platform, it covers the distance which is equal to the sum of lengths of the train and platform

Given : The train takes 20 seconds to cross the platform.

So, the sum of lengths of train and platform

= speed of the train ⋅ time

= 300 meters

length of train + length of platform = 300

160 + length of platform = 300

length of platform = 300 - 160

= 140 meters

Hence the lengths of the train and platform are 160 m and 140 m respectively.

Problem 5 :

Two trains running at 60 km/h and 48 km/h cross each other in 15 seconds when they run in opposite direction. When they run in the same direction, a person in the faster train observes that he crossed the slower train in 36 seconds. Find the length of the two trains (in meters).

When two trains are running in opposite direction,

relative speed = 60 + 48

= 108 ⋅ 5/18 m/sec

Sum of the lengths of the two trains is sum of the distances covered by the two trains in the above relative speed.

Then, sum of the lengths of two trains is

= speed ⋅ time

= 30 ⋅ 15

When two trains are running in the same direction,

relative speed = 60 - 48

= 12 ⋅ 5/18

= 10/3 m/sec

When the two trains running in the same direction, a person in the faster train observes that he crossed the slower train in 36 seconds.

The distance he covered in 36 seconds in the relative speed is equal to the length of the slower train.

length of the slower train = 36 ⋅ 10/3 = 120 m

length of the faster train = 450 - 120 = 330 m

Hence, the length of the two trains are 330 m and 120 m.

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Quantitative Aptitude
Problems On Trains

Problems on Trains Concepts

Problems on Trains concepts are important for placement exams. Our industry professionals have discussed the concept of Problems on Trains in a sequence-specific manner.

Understanding the Concepts of Problems on Trains

As previously discussed, train problems are a basic sub-concept of relative Speed, which falls under the topic of Time, Speed, and Distance .

First and foremost, we must have a fundamental conceptual understanding of the relationship between Time, Speed, and Distance.

Let us understand the meaning of these concepts/terms one by one

Speed is a motion concept that describes how slowly or swiftly an item moves. Speed is defined as the distance divided by Time. Speed is measured in m/s, km/hr

Speed = Distance / Time

Time can be defined in physics by its unit of measurement - time is the reading on a clock. In classical, non-relativistic physics, it is a scalar quantity and measured in seconds (s), minutes (min), and hours (hr)

3. Distance

Distance refers to an object's total movement, independent of direction. The amount of area covered by an item, independent of its beginning or finishing location, can be described as distance. It is measured in Metre (m), kilometre (km), miles, feet.

4. Unit Conversion

We are required to convert all the parameters in a single unit in some of the Time Speed and Distance problems where speed is given in one unit and distance is provided in another.

The following conversion formula can assist you in accomplishing this.

Speed conversion from km/hr to m/s and viceversa

1 kilometre equals 1000 m , and 1 hour equals 3600 seconds.

Therefore, 1 km/hr = 1000m/3600s = 5/18 m/s.

So, to translate the speed from kmph to m/s

Multiply the given speed with 5/18

And to convert the speed from m/s to kmph

Multiply the given speed with 18/5.

5 . Concept of Relative Speed

The concept of relative speeds can be applied when two things are heading towards each other or in the same direction, one after the other.

In terms of relative speed,

If two objects are moving from opposing directions towards each other, always add their speeds.

When two objects are moving in the same direction, following each other, always subtract their speeds.

Example Problem

Two trains are travelling in opposite directions at speeds of 20 and 30 metres per second. Their respective lengths are 500m and 300m. The slower train takes the following seconds to cross the quicker train:

Because time taken is required in this problem, the formula for time taken is

Time required = Distance / Speed

In the provided example, distance is just the length of the trains, and speed is determined by the relative speed. Because both trains are heading in opposing directions, we must add their speeds.

⇒ Time taken = (500m+300m)/ (20+30)

⇒ Time Taken = 800/50

⇒ 16 Seconds

Why is understanding the concepts of Problems on Trains important?

Understanding the concepts of Problems on Trains assists in:

Understanding how Problems on Trains formulas are derived

Addressing the Problems on Trains problems promptly and accurately.

Resolving each of the various forms of questions on Problems on Trains topic

Developing your unique shortcuts

Is it possible to solve Problems on Trains without knowing the concepts?

Yes, it's possible to solve Problems on Trains questions without understanding what they entail. However, experts advise that comprehending the fundamentals is essential to address the Train problems effectively.

What is the right way to learn Problems on Trains concepts?

The foundation of mathematics is concepts, and understanding them is critical to boosting your performance in the Quantitative Aptitude section . Visualising the Problems on Trains concepts using real-life examples is the best approach to learn the Problems on Trains concepts.

Two trains leaving the station at different times...

Two trains are driving toward one another. The first train leaves Town A at 5am traveling at 60 miles per hour. The second train leaves Town B at 7am traveling at 70 miles per hour. the distance between Town A and Town B is 455 miles. What is the EXACT time that the collision will occur?

4 Answers By Expert Tutors

Gene G. answered • 08/13/13

Retired Electrical Engineer - ACT Prep, Free Official Practice Tests

The trick with word problems is to pick them apart to see what you know, then build equations that you can solve. It takes some practice.

In this problem, we know that one train starts two hours before the other one and travels at a known rate. Let's calculate how far it goes in those two hours:

d = rt = 2 hrs * 60 mi/hr = 120 mi The time is now 7:00 and the trains are 455 - 120 = 335 mi apart.

Now both trains are moving, one traveling at 60 mi/hr and the other at 70 mi/hr. Their closing speed is just 60 + 70 = 130 mi/hr, and the total distance to go is 335 mi.

Solve the rate equation for t to get t = d/r. Plug in 335 for d and 130 for r. Time to collision is t = 325 / 130 = 2.5769 hrs.

That's 2 hours with a remainder of 0.5769 0.5769 * 60 minutes = 34.615 minutes 0.615 * 60 seconds = 37 seconds

The time of collision will thus be the sum of 2 hrs + 2.5769 hrs added to the 5:00 starting time. T c = 5:00 + 4.5769 = 5:00 + 4:00 + 0:34 + 0:00:37 = 9:34:37

Sometimes, a problem will even ask where they would meet. Once you get to the point where you know the total travel times of both trains and their travel times, you could calculate how far each one went and find the exact location where they meet. You can treat each train's distance as a separate problem since you now know what each one did independently of the other. Try it! To check, their distances added together should be 455 when you're finished.

I hope this is helpful.

Brad M. answered • 08/13/13

Lines, Parabolas, Cubics, Polynomials, Sine Waves, and Exp-Log Curves

Hey Evan -- here's the "play by play" ... Train A goes 120mi from 5-7am, leaving a 335mi gap ... after 7am, the gap closes at 130mph ... "stair-step" ... 8am, 205mi left ... 9am, 75mi remains ... 9:30am, 10mi left -- need 1/13 more of an hour ... 60min/13 = 4.6 mins ==> crash at 9:34:35 :)

Patricia S. answered • 08/13/13

Math Tutoring for K-12 & College

Word problems can be tough. The best way that I've found to approach this type of question is by drawing a picture. Here's mine:

[Train #1] --> *Boom* <-- [Train #2]

(Town A = Mile #0) (Town B = Mile #455)

So if Train #1 is traveling at 60 miles per hour, the distance that this train travels can be represented by the equation d = 60 x ( d is distance, x is the number of hours the train has been traveling). Seeing as how I chose for Town A to be at mile #0, the equation d = 60 x also tells us how far Train #1 is from Town A.

Likewise, Train #2 is traveling at 70 miles per hour, so the distance this train travels can be represented by the equation d = 70 x (the variables mean the same thing). However, the equation d = 70 x does NOT represent the distance Train #2 is from Town A, because it left from Town B. Instead, if we write the left side of the equation as 455- d , we are able to find out how far Train #2 is from Town A. Our new equation for Train #2 is 455- d = 70 x .

The question wants you to figure out when the trains are at the exact same point on the tracks (in my picture above, when the trains go *Boom* :) ). In other words, when are both trains the same distance away from Town A. Now, the trains don't leave their stations at exactly the same time, so we can't just replace the d in Train #2's equation with 60x. Somehow, we have to represent the time difference in their departure in one or both of the equations. Here's a nice table to demonstrate the issue:

HOW FAR AWAY EACH TRAIN IS FROM TOWN A

Train #1 Train #2

5AM 0 -- <-- Train #1 leaves the station at Town A, but hasn't traveled any miles yet, so it is 0 miles away from Town A.

6AM 60 --

7AM 120 455 <-- Train #2 leaves the station at Town B, but hasn't traveled any miles yet, so it is 455 miles away from Town A.

8AM 180 455-70=385

9AM 240 385-70=315

10AM 300 315-70=240 <-- Somewhere between 9AM and 10AM, our two trains hit each other.

Let's look at our equation for Train #1 again: d = 60 x.

When Train #2 begins to travel, Train #1 has already traveled 120 miles away from Town A (See table above.). If we write our equation for Train #1 as d = 60 x + 120, now both this equation and the equation that we have for Train #2 refer to the distance each train is away from Town A, starting at 7AM (the first time that BOTH trains are traveling).

So, to recap:

Train #1 equation: d = 60 x + 120 ; Train #2 equation: 455 - d = 70 x

Both equations use the same meaning for d and for x , so your next step would be to combine them into one equation and solve for x (which should be the only variable left in your combined equation). Let me know if you need more help or if you have any questions about the explanation thus far.

Danielasdf B. answered • 08/13/13

"English, SPSS, And Biology Tutor"

The first train travels 60 miles from 6am to 7am So at 7am the trains are 455 - 60 = 395 miles apart First train: Distance from town A (DA) = Velocity* time = 60t Second train: Distance from town B (DB) = Velocity*time = 70t So, DA + DB = 60t + 70t 395 = 130t t = 395/130 = 3.4 hrs = 3 hrs 4 mins The first train left at 5am so the exact time would be 8:04am (5am +3 hrs and 4 minutes)

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Aptitude - Problems on Trains

Why should i learn to solve aptitude questions and answers section on "problems on trains".

Learn and practise solving Aptitude questions and answers section on "Problems on Trains" to enhance your skills so that you can clear interviews, competitive examinations, and various entrance tests (CAT, GATE, GRE, MAT, bank exams, railway exams, etc.) with full confidence.

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Here you can find multiple-choice Aptitude questions and answers based on "Problems on Trains" for your placement interviews and competitive exams. Objective-type and true-or-false-type questions are given too.

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You can easily solve Aptitude quiz problems based on "Problems on Trains" by practising the given exercises, including shortcuts and tricks.

Problems on Trains - Formulas
Problems on Trains - General Questions
Problems on Trains - Data Sufficiency 1
Problems on Trains - Data Sufficiency 2
Problems on Trains - Data Sufficiency 3

Speed =		60 x	5		=		50
			18				3

Length of the train = (Speed x Time).

		50	x 9
		3

Speed of the train relative to man =		125
		10

=		25
		2

=		25	x	18
		2		5

= 45 km/hr.

Let the speed of the train be x km/hr. Then, relative speed = ( x - 5) km/hr.

Speed =		45 x	5		=		25
			18				2

Time = 30 sec.

Let the length of bridge be x metres.

Then,	130 +	=	25
	30		2

Video Explanation: https://youtu.be/M_d8WufJWKc

Let the speeds of the two trains be x m/sec and y m/sec respectively.

Then, length of the first train = 27 x metres,

and length of the second train = 17 y metres.

	27 + 17	= 23
	+

		=	3	.
			2

Speed =		54 x	5
			18

Length of the train = (15 x 20)m = 300 m.

Let the length of the platform be x metres.

Then,	+ 300	= 15
	36

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Physics Problems with Solutions

Velocity and speed: solutions to problems.

A man walks 7 km in 2 hours and 2 km in 1 hour in the same direction. a) What is the man's average speed for the whole journey? b) What is the man's average velocity for the whole journey? Solution to Problem 1: a)

= 3 km/h

= 3.2 km/h (approximated to the nearest tenth)

= 1.5 km/h

You start walking from a point on a circular field of radius 0.5 km and 1 hour later you are at the same point. a) What is your average speed for the whole journey? b) What is your average velocity for the whole journey? Solution to Problem 3: a) If you walk around a circular field and come back to the same point, you have covered a distance equal to the circumference of the circle.

= Pi km/h = 3.14 km/h (approximated)

John drove South 120 km at 60 km/h and then East 150 km at 50 km/h. Determine a) the average speed for the whole journey? b) the magnitude of the average velocity for the whole journey? Solution to Problem 4: a)

= 54 km/h

= 38.4 km/h (approximated)

If I can walk at an average speed of 5 km/h, how many miles I can walk in two hours? Solution to Problem 5: distance = (average speed) * (time) = 5 km/h * 2 hours = 10 km using the rate of conversion 0.62 miles per km, the distance in miles is given by distance = 10 km * 0.62 miles/km = 6.2 miles

A train travels along a straight line at a constant speed of 60 mi/h for a distance d and then another distance equal to 2d in the same direction at a constant speed of 80 mi/h. a)What is the average speed of the train for the whole journey?

= 72 mi/h

A car travels 22 km south, 12 km west, and 14 km north in half an hour. a) What is the average speed of the car? b) What is the final displacement of the car? c) What is the average velocity of the car?

Solution to Problem 7: a)

= 96 km/h

= 28.8 km/h (approximated)

Solution to Problem 8: a)

= 2 m/s

= 1.5 m/s (approximated)

Train Problems, Check Example, Formulas, Shortcuts

Train Problems

Problems on train are a common topic in competitive exams, particularly in tests related to quantitative aptitude and reasoning. These problems are designed to test the candidate’s ability to solve numerical problems related to train travel, such as distance, speed, time, and acceleration. In this article, we will explore some common types of problems on train that are likely to appear in competitive exams and how to solve them.

Train Problems Example

Distance and Speed Problems One of the most common types of problems on train that appear in competitive exams involves calculating the distance, speed, or time taken by a train to travel a certain distance. For example, a question may ask how long it takes for a train traveling at a speed of 60 km/hr to cover a distance of 240 km. To solve this problem, we can use the formula:

Time taken = Distance / Speed

In this case, the time taken would be:

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Time taken = 240 km / 60 km/hr = 4 hours

Another variation of this type of problem involves two trains traveling towards each other on the same track, starting from different points. In this case, we can use the formula:

Time taken = Total Distance / Total Speed

For example, if two trains are traveling towards each other at speeds of 50 km/hr and 60 km/hr respectively and the distance between them is 300 km, we can calculate the time taken for them to meet as follows:

Total speed = 50 km/hr + 60 km/hr = 110 km/hr Time taken = 300 km / 110 km/hr = 2.73 hours

Time and Rate Problems Another common type of problem on train that appears in competitive exams involves calculating the speed or rate of the train based on the time taken to cover a certain distance. For example, a question may ask what the speed of a train is if it takes 2 hours to cover a distance of 120 km. To solve this problem, we can use the formula:

Speed = Distance / Time

In this case, the speed would be:

Speed = 120 km / 2 hours = 60 km/hr

Another variation of this type of problem involves calculating the distance covered by the train based on the time taken to travel at a certain speed. In this case, we can use the same formula as before:

Distance = Speed * Time

For example, if a train is traveling at a speed of 80 km/hr and it takes 3 hours to reach its destination, we can calculate the distance covered as follows:

Distance = 80 km/hr * 3 hours = 240 km

Average Speed Problems Calculating the average speed of a train over a certain distance is another common type of problem on train that appears in competitive exams. For example, a question may ask what the average speed of a train is if it travels a distance of 400 km in 8 hours. To solve this problem, we can use the formula:

Average speed = Total distance / Total time taken

In this case, the average speed would be:

Average speed = 400 km / 8 hours = 50 km/hr

Another variation of this type of problem involves finding the average speed of the train over two different distances. For example, if a train travels at a speed of 60 km/hr for the first half of its journey and at a speed of 80 km/hr for the second half, we can calculate the average speed as follows:

Total distance = Distance for the first half + Distance for the second half = 0.5D + 0.5D = D

Total time taken = Time taken for the first half + Time taken for the second half

Time taken for the first half = Distance / Speed = 0.5D / 60 km/hr = D / 120 km/hr Time taken for the second half = Distance / Speed = 0.5D / 80 km/hr = D / 160 km/hr

Total time taken = D / 120 km/hr + D / 160 km/hr = 2D / (3/2 + 4/5) km/hr = 720D / 29 km/hr

Average speed = Total distance / Total time taken = 2D / (720D / 29) km/hr = 58.125 km/hr

Relative Speed Problems Relative speed problems on train involve calculating the speed or distance between two trains traveling in opposite directions or the same direction. For example, a question may ask what the relative speed of two trains is if one is traveling at 50 km/hr and the other is traveling at 60 km/hr in the opposite direction. To solve this problem, we can simply add the speeds of both trains:

Relative speed = Speed of train 1 + Speed of train 2

In this case, the relative speed would be:

Relative speed = 50 km/hr + 60 km/hr = 110 km/hr

Another variation of this type of problem involves calculating the distance between two trains if they are traveling towards each other. For example, if two trains are traveling towards each other at speeds of 40 km/hr and 60 km/hr respectively and the distance between them is 200 km, we can calculate the time taken for them to meet as follows:

Relative speed = Speed of train 1 + Speed of train 2 = 40 km/hr + 60 km/hr = 100 km/hr Time taken = Distance / Relative speed = 200 km / 100 km/hr = 2 hours

Acceleration Problems Acceleration problems on train involve calculating the time taken by a train to reach a certain speed or distance. For example, a question may ask how long it takes for a train to reach a speed of 100 km/hr if it accelerates at a rate of 10 km/hr^2. To solve this problem, we can use the formula:

Time taken = (Final speed – Initial speed) / Acceleration

Time taken = (100 km/hr – 0 km/hr) / 10 km/hr^2 = 10 hours

Another variation of this type of problem involves calculating the distance covered by the train in a certain time, given its initial speed and acceleration rate. In this case, we can use the formula:

Distance = Initial speed * Time + 0.5 * Acceleration * Time^2

For example, if a train is traveling at a speed of 20 km/hr and accelerates at a rate of 5 km/hr^2 for 2 hours, we can calculate the distance covered as follows:

Distance = 20 km/hr * 2 hours + 0.5 * 5 km/hr^2 * (2 hours)^2 = 50 km

Train Problems for SSC CHSL – Download Free E-book

Sneak peak of train problems for ssc chsl e-book.

Train Problems for SSC CHSL

1. Two trains of equal length are running on parallel lines in the same direction at the rate of 46 km/h f and 36 km/h. The faster train passes the slower J train in 36 s. The length of each train is

2. A train 300 m long is running with a speed of 54 km/h. In what time will it cross a telephone pole?

3. Two trains of length 180 meters with velocity 30 m/s and 60 m/s travel in opposite directions and if the initial distance between them is 0.54 kilometers then what is the time taken for their tails to cross each other?

4. A train moves at a speed of 108 kmph. Its speed in meters per second is:

C) 18

5. A train moves past a telegraph post and a bridge 264 m long in 8 seconds and 20 seconds respectively. What is the speed of the train?

A) 79.2 km/hr

B) 79 km/hr

C) 70 km/hr

D) 69.5 km/hr

6. A train travels a distance of 480 km at uniform speed. Due to breakdown, its speed is reduced by 10 km/hr and hence it travels the destination 8 hours late. Find the initial speed of the train.

A) 20 km/hr

B) 35 km/hr

C) 25 km/hr

D) 30 km/hr

7. A train travelling with constant speed crosses a 96 m long platform in 12 sec and another 141 m long platform in 15 sec. The length of the train and its speed are

A) 84 m, 54 km/h

B) 84 m, 60 km/h

C) 64 m, 54 km/h

D) 64 m, 44 km/h

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SSC CGL Syllabus 2024 and Exam Pattern

Train Problems Formula

The formula for calculating train problems can vary depending on the specific context and type of problem being addressed. However, some common formulas that may be used include:

Distance = Speed x Time: This formula is commonly used to calculate the distance that a train can travel based on its speed and the time it takes to complete the journey.
Acceleration = Change in Velocity / Time Taken: This formula is used to calculate the rate at which a train can accelerate or decelerate, based on the change in its velocity over a given time period.
Braking Distance = (Initial Speed ^ 2 – Final Speed ^ 2) / (2 x Deceleration): This formula is used to calculate the distance that a train will need to come to a complete stop, based on its initial speed, final speed, and the rate at which it can decelerate.
Power = Force x Velocity: This formula is used to calculate the amount of power required to move a train at a given velocity, based on the force required to overcome resistance and maintain motion.
Train Capacity = Number of Cars x Passenger Capacity per Car: This formula is used to calculate the maximum number of passengers that a train can carry, based on the number of cars it has and the passenger capacity per car.

Train Problems Shortcuts

Here are some shortcuts that can be useful in solving train problems quickly:

If two trains are moving in the same direction, the relative speed between them is the difference between their speeds. Example: If train A is moving at 60 km/hr and train B is moving at 40 km/hr in the same direction, their relative speed is 60 – 40 = 20 km/hr.
If two trains are moving in opposite directions, the relative speed between them is the sum of their speeds. Example: If train A is moving at 50 km/hr and train B is moving at 70 km/hr in opposite directions, their relative speed is 50 + 70 = 120 km/hr.
The time taken by a train to pass a stationary object (such as a pole or a platform) is equal to the length of the train divided by its speed. Example: If a train of length 150 meters passes a pole in 15 seconds, its speed is (150/15) m/s = 10 m/s or 36 km/hr.
The time taken by two trains to cross each other is equal to the sum of their lengths divided by the sum of their speeds. Example: If two trains of lengths 200 meters and 250 meters respectively cross each other in 20 seconds, their speeds are (200+250)/20 m/s = 22.5 m/s or 81 km/hr.

By using these shortcuts, one can quickly solve train problems without having to write down and solve long equations.

Train Problems – Conclusion

In conclusion, problems on train are a common topic in competitive exams, particularly in tests related to quantitative aptitude and reasoning. By understanding the formulas and techniques used to solve these problems, candidates can increase their chances of success in these exams.

Ans. The formula for calculating train problems can vary depending on the specific context and type of problem being addressed. for more information read the full article.

Ans. No, you can’t download pdf but you can bookmark this page for future use case.

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Problems on Trains: Definition, Rules, Solved Examples, Formulas

Questions on speed, time, and distance are common in quantitative aptitude section of most government job exams and bank exams. Among these, problems on trains , particularly concerning the speed of train, the distance traveled by the train, and the time taken by the train to traverse a particular distance are quite popular. Other common types of questions asked include ones when two trains are moving in the same direction or in opposite directions. The problems on trains must be considered as a special case because trains are considerably long structures. We solve these problems using the concept of linear equations in two variables. Let us discuss the problems related to trains and their formulas one by one.

Introduction to Speed, Time, Distance Formula

Speed is defined as the time taken by an object to cover a unit distance (1 meter or 1 kilometre). It can be measured as the ratio of the distance travelled by a body in a given period.

The SI unit of speed is $\rm{meter/second}$; however, the commonly used unit of speed in daliy life is $\rm{kilometre/hour}$.

$ {\text{Speed=}}\frac{ { {\text{Distance}}}}{ { {\text{Time}}}}$

To calculate the distance covered by the object or the time taken to cover the distance, we can use the speed formula by substituting the values of the known quantities in it.

$ {\text{Distance=Speed} \times \text{Time}}$

$ {\text{Time=}}\frac{ { {\text{Distance}}}}{ { {\text{Speed}}}}$

We will use the same concept to solve the problems on trains. We also calculate the relative speed of two trains moving in the opposite direction and same direction.

Application of Equations in Problem on Trains

Consider two trains moving in the same or opposite direction. To find the distance travelled by the trains and the time is taken, we need to know the relative speed. In these types of problems, there will be some known and unknown quantities. To determine the unknown quantity such as time, distance and speed, we need to form an equation. Solving the equation, we can get the value of an unknown quantity.

Formulas for Problem on Trains

We know that,

$ {\text{Speed of the train}} = \frac{ { {\text{Total distance covered by the train}}}}{ { {\text{Time taken}}}}$

Before we talk about the formulas of problems on trains, some related terms are needed to discuss.

We can convert a $\rm{kilometre/hour}$ to a $\rm{meter/second}$ by multiplying it with $\frac{5}{ {18}}.$

We know that $1\,\rm{kilometer} = 1000\,\rm{meter}$ and $1\,\rm{hour} = 60 × 60 = 3600\,\rm{second}$

Now, $\frac{ {1\,{\text{kilometre}}}}{ {1\,{\text{hour}}}} = \frac{ {1000\,{\text{metre}}}}{ {3600\,{\text{second}}}} = \frac{5}{ {18}}\,{\text{metre/second}}$

The Relative Speed of Two Trains moving in the Same Direction

The relative speed will be the difference between their speed if two trains move in the same direction.

The Relative Speed of Two Trains moving in the Opposite Direction

The relative speed will be the sum of their speed if two trains move in the opposite direction.

Distance Travelled when Two Trains are moving in the Same Direction/Opposite Direction

For both cases, the trains will cover the distance that is equal to the sum of the lengths of two trains.

Distance Travelled when a Train crosses a Stationary Object

When a train crosses a stationary object such as a pole, a standing person, it will cover the distance that is equal to its length.

Distance Travelled when a Train crosses a Platform/a Bridge

When a train crosses a platform or a bridge, it will cover the distance that is equal to the sum of the length of the train and bridge or platform.

Formula of Time when $2$ Trains moving in the Opposite Direction

If the two trains are moving in opposite directions with a speed of $x$ and $y$ and the length of two trains are, $a$ and $b$ respectively.

Then, the time taken by the trains to cross each other $ = \frac{{a + b}}{{x + y}}$

The Formula of Time when the Two Trains moving in the Opposite Direction

Note: As the trains are running in the opposite direction, the relative speed is $x + y$.

Formula of Time when $2$ Trains moving in the Same Direction

If the two trains are moving in the same direction with a speed of $x$ and $y$ and the length of two trains are $a$ and $b$ respectively.

Then, the time taken by the trains to cross each other $ = \frac{{a + b}}{{x – y}}$

Note: As the trains are running in the opposite direction, the relative speed is $x – y$.

Formula of Time When a Train Crosses a Pole

If a train of length $a$ moving with a speed $x$, crosses a pole or a person, then the time taken to cross the pole $ = \frac{a}{x}$

Formula of Time When a Train Crosses a Bridge or a Platform

If a train of length $a$ moving with a speed $x$, crosses a platform/bridge of length $b$ then the time taken to cross the platform/bridge $ = \frac{a + b}{x}$

Solved Example Probelms on Problem on Trains

Q.1. A train running at the speed of $36\,\rm{km/hr}$ crosses a stationary object in . Find the length of the train. Ans: Given, speed of the train is $36\,\rm{km/hr}$. We know that when a train crosses a stationary, it covers the distance equal to its length. Now, $\rm{Distance = Speed} \times \rm{Time}$ Therefore, the length of the train $ = \frac{ {36 \times 10}}{ {60 \times 60}} = 0.1\, {\text{km}} = 0.1 \times 1000\, {\text{m}} = 100\, {\text{m}}$

Q.2. A train moving at $90\,\rm{kmph}$ crosses another train moving in the same direction at $180\,\rm{kmph}$ in $30\,\rm{seconds}$. Find the sum of the lengths of both the trains. Ans: Speed of train $A = 90\, {\text{kmph}} = 90 \times \frac{ {1000}}{ {3600}} = 90 \times \frac{5}{ {18}} = 25\, {\text{m}}/ {\text{sec}}$ Speed of train $B = 180\, {\text{kmph}} = 180 \times \frac{5}{{18}} = 50\, {\text{m}}/ {\text{sec}}$ The relative speed will be the difference between their speed if two trains move in the same direction The relative speed $ =( 50-25)\,\rm{m/sec} = 25\,\rm{m/sec}$ The time taken by train $A$ to cross the train $B = 30\,\rm{secs}$ When the trains are moving in the same direction, the trains will cover the distance that is equal to the sum of the lengths of two trains. $\rm{Distance = the}\,\rm{sum}\,\rm{of}\,\rm{the}\,\rm{length}\,\rm{of}\,\rm{two}\,\rm{trains} = \rm{Speed} \times \rm{Time} = 25 × 30\,\rm{m}= 750\,\rm{m}$ Hence, the sum of the lengths of both the trains is $750\,\rm{m}$.

Q.3. Two trains of equal length are running on parallel lines in the same direction at $40\,\rm{km/hr}$ and $30\,\rm{km/hr}$. The faster train passes, the slower train in $36\,\rm{seconds}$. Find the length of each train. Ans: Let us say the length of the trains is $x\,\rm{m}$, and the distance covered by it is $(x + x) = 2x\,\rm{m}$ The relative speed of the trains $ = (40 – 30)\, {\text{kmph}} = 10\, {\text{kmph}} = 10 \times \frac{5}{ {18}} = \frac{ {25}}{9}\, {\text{m}}/ {\text{sec}}$ Speed of the faster train$ = \frac{2x}{36}$ So, $ \frac{2x}{36} = \frac{25}{9} $ or, $ x = \frac{25 \times 36}{18} = 50\,\rm{m}$ Hence, the length of each train is $50\,\rm{m}$.

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Q.4. It takes $12\,\rm{seconds}$ for a $360\,\rm{m}$ long train to pass a pole. How long will it take to pass a platform of $540\,\rm{m}$ long? Ans: We know that, Speed of the train $= \frac{ { {\text{Total distance covered by the train}}}}{ { {\text{Time taken}}}}$ Speed of the train $=\frac{ {360}}{ {12}}\,\rm{m/sec} = 30\,\rm{m/sec}$ When a train crosses a platform, it will cover the distance that is equal to the sum of the length of the train and the platform. The time taken to pass a platform is $ = \frac{ {360 + 540}}{ {30}} = \frac{ {900}}{ {30}} = 30 {\text{}}\, {\text{seconds}}$

Q.5. A train $350\,\rm{m}$ long is running at a speed of $54\,\rm{km/hr}$. In how much time will it pass a bridge $100\,\rm{m}$ long? Ans: Speed of the train $ = 54\, {\text{km}}/ {\text{hr}} = 54 \times \frac{5}{ {18}} = 15\, {\text{m}}/ {\text{sec}}$ The total distance that needs to be covered by the train $= (350 + 100)\,\rm{m} = 450\,\rm{m}$ $ {\text{Time=}}\frac{ { {\text{Distance}}}}{ { {\text{Speed}}}}$ Hence,the time is taken by the train to pass the bridge $ = \frac{ {450}}{ {15}} = 30\, {\text{seconds}}$

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In this article, we have covered how to solve the problems on trains when two trains move in opposite direction/ same direction when a train crosses a stationary object/bridge/platform, the relative speed of two trains, and the relative speed of two trains.

Frequently Asked Questions (FAQ) – Problem on Trains

The frequently asked questions about problems on trains are answered here:

For solving the problems related to trains, it is essential to know the relative speed of two trains. If two trains move in the same direction, then the relative speed will be the difference between their speed. If two trains move in the opposite direction, then the relative speed will be the sum of their speed.
For both cases, the trains will cover the distance equal to the sum of the lengths of two trains.

If the two trains run in opposite directions with a speed of $x$ and $y$ and the length of two trains are $a$ and $b$ respectively.
So, the time taken by the trains to cross each other $ = \frac{{a + b}}{{x + y}}$
If the two trains run in the same direction with a speed of $x$ and $y$ and the length of two trains are, $a$ and $b$ respectively.
So, the time taken by the trains to cross each other $ = \frac{{a + b}}{{x – y}}$
If a train of length $a$ moving with a speed $x$, crosses a pole or a person then the time is taken to cross the pole $ = \frac{{a}}{{x}}$
If a train of length $a$ moving with a speed $x$, crosses a platform/bridge of length $b$ then the time is taken to cross the platform/bridge $ = \frac{{a + b}}{{x}}$

The problems on trains are similar to the speed, time, and distance problems. If we know the relative speed of the trains and the length of the trains, we can easily find out the time taken to cover the distance and vice versa.

We can convert $1\,\rm{km/hr}$ into $\rm{m/sec}$ by multiplying it by $ = \frac{{5}}{{18}}.$

If the distance covered by the train and the time taken to cover the distance is known, we can find the train’s speed as
${\text{Speed of the train}} = \frac{{{\text{Total distance covered by the train}}}}{{{\text{Time taken}}}}$

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We hope this detailed article on Problems on trains is helpful to you. If you have any queries, ping us through the comment box below and we will get back to you as soon as possible.

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GMAT Problems on Trains

Updated on
Nov 17, 2022

If you are practising to ace competitive exams like GRE or GMAT then logical reasoning is one section that you really need to focus on. Logical reasoning is a part of almost every competitive exam and students usually have a hard time solving that section of the question paper but with correct tricks and proper guidance and practice, you can easily solve that section in no time. Problems on trains are among the popular examination questions, every entrance exam usually has a few questions that involve problems related to trains, their speed, direction, and length. This blog will try to simplify and explain this section of the paper in order to give you a basic idea of how to go about problems on trains.

Problems on Trains: Concepts and Logics

The problems on trains follow a certain format that revolves around some fundamental concepts, these are:

Distance and time

The question based on trains usually includes concepts like relative motion, speed and time. If you are good in physics or even if you remember the basic concepts of it then you can easily ace this section. There are questions that involve distance and time. One formula that you need to keep in mind is d= st, where d is distance, s is the speed and t stands for time. Let’s look at a question which involves this formula:

Question : Train A travels at 50 mph, Train B travels at 70 mph. Taking into account that both trains leave the station at the same time, evaluate how far apart they will be after two hours?

Solution : To calculate the distance here you need to add the distance traveled by both the trains together.

Distance traveled by train A will be: d= s t, the rate at which it travels here is 50mph and the time is 2 hours.

So the distance traveled by train A will be 50×2 = 100.

Similarly, distance traveled by train B will be 70×2 = 140.

Now if we add the distances 140+100= 240, hence the distance at which they travel apart from each other would be 240 miles.

If the trains are traveling in the same direction then we would subtract distances traveled by both the trains i.e. 140-100= 40, then the answer would be 40 miles.

Length of the train

In these type of questions, you need to find out the length of the train with the given information in the question. These questions usually include relative speed and the formula used here is the same d= st. Let’s look at an example in order to understand the problem more clearly.

Question : A train is traveling at a speed of 60kmph it then overtakes a bike that is traveling at 30kmph in about 50 seconds. Now calculate the length of the train.

Solution : To calculate the length of the train we need to find out the distance traveled by the train, since the bike is also in motion we need to look at the relative speed of the bike and the train.

Since both the objects are moving in the same direction we need to subtract the distance traveled by both the objects i.e. 60-30= 30, so the relative speed is 30kmph.

Now let’s find out the distance traveled by train while taking over the bike, applying the formula, d= st, distance will be 30kmphx50 seconds. Now let’s convert the distance into meter per second.

1 kmph = 5/18 m/sec

Therefore 30kmph= 30×5/18= 8.33 m/sec

Therefore distance traveled will be 8.33×50= 416.5 meters, the length of the train is 416.5 meters.

Types of Questions: Problems on Train

The number of applicants has increased throughout the years, and each year, candidates observe a new pattern or format in which questions are asked for various topics in the syllabus.

In order to minimise the chance of receiving a bad grade, candidates should be aware of the several ways questions may be phrased or asked throughout the exam.

As a result, the types of questions that might be posed from train-based challenges are listed below:

Time Taken by Train to Traverse Any Stationary Body or Platform – A question may require the applicant to determine the amount of time it takes a train to cross a particular type of stationary object, such as a pole, a standing person, a platform, or a bridge.
Time it takes for two trains to cross paths – The duration it might take for two trains to cross each other is still another possible inquiry.
Train Equation-Based Problems- The question may present two situations, and the candidates must build equations based on the conditions.

Key Formulas For Problems on Train

A candidate must memorise the relevant formulas in order to solve any numerical ability question so they can respond quickly and effectively.

The following key formulas for train-related questions will aid candidates in responding to questions based on this subject:

Speed of the Train = Total distance covered by the train / Time taken
The time it takes for two trains to cross each other is equal to (a+b) / (x+y) if the lengths of the trains, say a and b, are known and they are going at speeds of x and y, respectively.
When the length of two trains, let’s say a and b, is known and they are travelling at speeds of x and y, respectively, in the same direction , the time it takes for them to cross each other is equal to (a+b) / (x-y).
When two trains begin travelling in the same direction from points x and y and cross each other after travelling in opposite directions for times t1 and t2, respectively, the ratio of the speeds of the two trains is equal to t2:t1.
If two trains depart from stations x and y at times t1 and t2, respectively, and they go at speeds L and M, respectively, then the distance from x at which they will collide is equal to (t2 – t1) (speed product) / (difference in speed).
When a train stops, it travels the same distance at an average speed of y rather than the normal average speed of x. Hourly Rest Time = (Difference in Average Speed) / (Speed without stoppage)
If it takes two trains of similar length and speed t1 and t2 to pass a pole, the time it takes for them to cross each other if the trains are going in the opposite direction is equal to (2t1t2) / (t2+t1).
If it takes two trains of equal length and speed t1 and t2 to cross a pole, the time it takes for the trains to cross each other if they are travelling in the same direction is equal to (2t1t2).

Things to Keep in Mind While Solving Problems on Trains

While solving the section related to problems on trains it is important to keep certain things in mind to ensure efficiency and accuracy. Here are a few things that you should keep in mind:

Make sure all the units are the same, if not don’t forget to change them.
Read the questions carefully and keep in mind the concepts of speed and relative speed.
Remember the basic formulas
Be clear about all the concepts.

Always read the question carefully before responding, as train-based topics are frequently given in a convoluted manner. Try to apply a formula after reading the question; this may lead to a quick solution and save you time.

When two bodies are moving in the same direction, the relative speed is equal to the difference in their speeds. For example, a person in a train travelling at 60 km/hr in the west will perceive the speed of the other train travelling at 40 km/hr as being 20 km/hr (60-40).

x km/h = x*(5/18) m/s. The amount of time needed for a train of length/meters to pass a pole, a single post, or a standing person is equal to the distance the train must go in/meters.

Understanding the concepts behind problems on trains can help you in developing strategies to solve those questions. While we have tried to give you all the important information required to tackle these questions, it is natural to feel stressed about the entrances. The experts at Leverage Edu can help you plan for these exams so that nothing comes between you and your dreams.

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Time, Speed and Distance: Problems on Trains

Important Points

When two trains are going in the same direction, then their relative speed is the difference between the two speeds.
When two trains are moving in the opposite direction, then their relative speed is the sum of the two speeds.
When a train crosses a stationary man/ pole/ lamp post/ sign post- in all these cases, the object which the train crosses is stationary and the distance travelled is the length of the train.
When it crosses a platform/ bridge- in these cases, the object which the train crosses is stationary and the distance travelled is the length of the train and the length of the object.
When two trains are moving in same direction, then their speed will be subtracted.
When two trains are moving in opposite directions, then their speed will be added.
In both the above cases, the total distance is the sum of the length of both the trains.
When a train crosses a car/ bicycle/ a mobile man- in these cases, the relative speed between the train and the object is taken depending upon the direction of the movement of the other object relative to the train- and the distance travelled is the length of the train.

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HS2 trains too high for station platforms – leaving taxpayers with £200m bill

The news comes days after it emerged that the trains will require a separate redesign to have extra doors added.

HS2 trains are too high for existing station platforms, i can reveal, in the latest mishap for the project that leaves taxpayers with another huge bill.

As the Chancellor Rachel Reeves mulls tax rises and spending cuts to balance the UK’s books, taxpayers will have to find another £200m to refit HS2 train carriages because their doors are too high for ordinary station platforms.

Industry sources told i that Network Rail and the Office for Rail and Road were unwilling to allow the 225mph trains to run on the existing network because of fears that the gap between the train and the platform will be too great, making them unsafe.

“There are grave concerns regarding the rolling stock,” a source told i , claiming that Network Rail was unlikely to allow the trains to run on their network due to safety concerns.

Insiders say that the decision by former prime minister Rishi Sunak to scrap the scheme north of Birmingham , means the trains have a greater exposure to the existing network, heightening concerns that they are unfit for use on Network Rail platforms.

HS2 Ltd, created to deliver the £57bn project , said the trains were still in the design phase, and would now be fitted with a “two-step” solution to manage concerns around the gap on conventional platforms.

The news comes just days after it emerged that the trains will require a separate redesign to have extra doors added on each carriage to shorten the time the trains are sitting on the platforms – known as “dwell times” – to allow passengers to alight.

Stations with platforms of concern Oxenholme Penrith Motherwell Runcorn Crewe Warrington Wigan Lancaster Macclesfield Stockport Glasgow Central

Documents seen by i show that cost estimates for all the redesigns were £188m in 2022, with HS2 Ltd assessments showing that there are issues with around 11 platforms scattered across the rail network where the high speed trains will run.

According to minutes from a meeting between HS2 Ltd executives and Network Rail executives, concerns were also raised about “diversity and inclusion” by pursuing a train design “which might not work for wheelchair users”.

Raising concerns, Network Rail’s chief engineer Amanda Hall is recorded as stating that “it is surprising that a manufacturer with a non-compliant train should win” the contract for manufacturing HS2 trains.

Ben Rule, a director of infrastructure at HS2 Ltd, responded that the high-speed train design is “complying with the contract, but whether the contract looked at this [issue with the trains] in the most compliant way is a question”.

HS2 Ltd has already submitted its request to redesign the trains, which are not due to be completed until 2027 and no pricing has been attached to the proposals.

Mind the gap Concerns around accidents involving passengers embarking or alighting trains at the platform edge has increased across the rail industry in recent years. The particular issue with HS2 trains stems from its original plan to use two types of high-speed trains, one known as “captive” trains and the other as “classic compatible” trains. Captive trains were due to operate solely on high-speed tracks, and were to be built to European dimensions, making them taller and wider and required bigger platforms. These trains would have their own platforms which are higher than those on Network Rail stations. The doors of the trains were designed to offer “step-free” access, meaning they align with the platform and are thus higher. Classic compatible trains were to be used to run on both HS2 and existing rail infrastructure. These are not as tall or wide as captive trains, but they must still serve HS2 platforms, which are higher than conventional platforms. These trains included a step to allow passengers to alight level with the platform, but a redesign is now necessary to include a two-step system, one which will be used on HS2 platforms and a second that will ensure passengers can get on and off the high speed trains safely on existing National Rail platforms.

But early estimations for the design changes from 2022 show that the redesigns could add a further £188,600,000 to the existing £2bn contract HS2 Ltd has secured with the joint venture manufacturers Hitachi and Alstom.

The initial HS2 project planned to use two different HS2 trains. One, larger high-speed train, which served only HS2 platforms, and another that would run on both high speed and existing tracks. As the rail project began to be cut back, beginning with the scrapping of the eastern leg of the rail line in 2021, the decision was taken to use just one train design.

The issue of passenger safety between trains and the platform has increased in recent years, with official figures showing that more than half of all passenger accidents occur between the train and platform, according to the Rail and Safety Standards Board.

A spokesman for HS2 Ltd said: “HS2’s new trains and stations are designed to work seamlessly together, providing the best possible street-to-seat service that will enable everyone, including those with limited mobility, to more easily use the high-speed railway.

“However, maintaining our trains’ improved accessibility standards along the West Coast Mainline is complicated by platform heights varying at different stations. Therefore, we’ve engineered a separate step to minimise the gap between train and platform.”

The Office for Rail and Road said it has no “current” concerns with the HS2 rolling stock.

“ORR has been making routine enquiries and continues to engage with HS2 regarding its approach to managing risks at the train and platform interface as we would with any company introducing new trains,” a spokesman said.

It follows reports that Sir Keir Starmer will consider reviving the scrapped routes north of Birmingham after receiving a Labour-commissioned infrastructure report.

The report on rail by former Siemens UK boss Juergen Maier was commissioned by Labour when in opposition, The Telegraph reported. Although an unofficial document, its suggestions that much of the HS2 project scrapped by Rishi Sunak in October should be revived would inform the Government when making decisions about rail projects.

HS2: Off the rails Originally conceived in 2009, high-speed 2 was to be built in phases and run from London to Birmingham, Manchester and Leeds, significantly adding capacity to the rail network and cutting journey times. The first phase would run from London to Birmingham, Phase 2a would run from Birmingham to Crewe and Phase 2b would build new lines from Birmingham to Leeds and Crewe to Manchester. But the scheme, which was at one stage the biggest infrastructure project in Europe, has been beset by delays and cost overruns as the dream of improved rail travel hit the reality of the planning system, political opposition, soaring construction costs and the pandemic. The first major signs of trouble came early on when the £20bn project in 2009, increased to £32.7bn in 2012, only to be revised upwards again by the Government in 2013 to £50bn. By 2019, a report by the then HS2 Ltd chair Allan Cook, revealed that the costs had ballooned to £88bn and would not be completed until 2040, seven years later than previously expected. Cost estimates were then pushed up once again in 2020, when it was judged that all three phases would come in at around £98bn in 2019 prices. By 2021, the Government scrapped the eastern leg of the scheme running from Birmingham to Leeds. Another fatal blow was delivered by Rishi Sunak in 2023, when he cancelled plans for the high-speed line to run north of Birmingham to Crewe and then to Manchester, despite already spending £2bn on Phase 2 of the line. A National Audit Office report in July revealed that nearly £600m was spent on buying land for Phase 2, while the Curzon Street Station in Birmingham will be built in full, despite less than half of the station platforms being used. Doubts also remain as to whether Phase 1 of the project will continue into Euston in central London, which risks leaving the UK’s major high-speed rail upgrade running a shuttle service from outside Birmingham to outside the capital.

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Why do electromagnetic train waves make MRI images inaccurate?

By Judd Boaz

By Madi Chwasta

Topic: Science and Technology

A photo of a Melbourne train platform overlaid with black and white static.

Electromagnetic interference from Melbourne's new train line is affecting hospital equipment. ( ABC News: John Graham )

Following reports that sensitive medical equipment at Melbourne hospitals were being affected by trains in the city's new underground metro line, Premier Jacinta Allan was not surprised.

The Age newspaper obtained leaked documents revealing electromagnetic waves from the Metro Tunnel testing had been interfering with the MRI machines in Parkville's hospital precinct, which includes the Royal Melbourne Hospital and the Peter MacCallum Cancer Centre.

"It’s a challenge that has been known for a number of years," Premier Allan said.

Pedestrians cross the road in front of the Peter MacCallum Cancer Centre

Leaked documents show medical equipment at the Peter MacCallum Cancer Centre in Parkville has been impacted by the new train line. ( ABC News: Scott Jewell )

"A number of years" may have been underselling the longstanding issue of electromagnetic interference, the phenomenon potentially affecting lifesaving machines.

The International Electrotechnical Commission — which sets global standards for electrical technologies — put together its first committee tackling electromagnetic interference in 1934.

In the 90 years since, our cities have become increasingly reliant on electricity and technology, and minimising the effects of electromagnetic interference has become more important.

But what is it, and how does it enable underground trains to affect crucial medical equipment?

What is electromagnetic interference?

Wherever an electric current flows, a magnetic field is generated — the stronger the current, the stronger the magnetic field.

It means all around us, wherever electricity is used, there are magnetic fields of varying strength.

The new Metro Tunnel project is producing electromagnetic interference. ( Victoria's Big Build )

Electromagnetic interference occurs when a stray magnetic field from one source disrupts the operation of another device.

A common example is when speakers hum or buzz when another electrical device like a mobile phone is nearby.

Electromagnetic interference can also affect things like television reception, giving rise to pixelation or other visual changes as the interference increases.

A hand holding a remote up to a black television screen.

Electromagnetic waves can interfere with TV reception. ( ABC Central West: Lauren Bohane )

While the appearance of static on a television set might be a small inconvenience, electromagnetic interference can also have serious negative effects on sensitive medical equipment like magnetic resonance imaging (MRI) machines and electron microscopes.

Such were the findings of the Victorian-Auditor General in 2022, who found that more than 17 machines at the Melbourne Biomedical Precinct were at risk from trains moving through the Metro Tunnel.

How is electromagnetic interference affecting MRI machines?

Magnetic resonance imaging scanners, or MRI machines, create a very strong magnetic field around a patient to create images of internal organs.

But the combination of strong magnetic fields and radio waves makes MRI machines a source of extremely high level electromagnetic emissions, and also makes them very susceptible to interference from external sources.

A train line, like the one being built in a subway under Royal Melbourne Hospital, represents a constant external source of electromagnetic interference.

Train lines, like the new Metro Tunnel, constantly produce electromagnetic interference. ( Victoria's Big Build )

The flow of currents to the trains in the overhead lines and the rails produces magnetic fields, which are then picked up by sensitive MRI machines.

The issue is one explored in 2020 by the California High Speed Rail Authority , who investigated the impacts of electromagnetic interference from trains on a planned project from Burbank to Los Angeles.

The authority found that for sensitive equipment such as MRI machines that were unshielded, electromagnetic interference is possible at distances of up to 60m.

It said 110m was the recommended separation distance between the machines and electric trains.

At its deepest, Melbourne's Metro Tunnel is just 40m underground.

MRI images can be affected by electromagnetic interference. ( Shutterstock: Atthapon Raksthaput )

Melbourne MRI radiographer Cleo Pilcher said the machines were very sensitive.

"We're very careful about what we take into the room, and sometimes roadworks outside have been known to interfere," she said.

Ms Pilcher said electrical interference could cause something known as an "artefact", which was a distortion or pattern interrupting the MRI image.

"You might be taking a picture of someone's knee, and you see this big white line over the image … you can't actually get any information out of the image."

How can interference be minimised?

Enclosing an MRI room with a Faraday cage is an way to limit electromagnetic interference, as it prevents the movement of these forces in and out of a room.

Dimuthu Wanasinghe, an expert in electromagnetic shielding from the University of Western Australia, said the cage had to be made from something that allowed the flow of an electrical charge, known as a conducting material.

"Think of [a Faraday cage] as a room surrounded by a conducting material, something like copper," Dr Wanasinghe said.

"If this room encounters an electromagnetic radiation, what happens is the conducting part will generate an electrical current that flows outside the room, so nothing inside the room will get affected."

A man stands next to an MRI machine while a person gets an xray.

MRI machines are contained in a room surrounded by a conductive material to create a Faraday cage. ( Supplied: Hunter Medical Research Institute )

Dr Wanasinghe said it was likely the Faraday cages in older hospital buildings were not built to shield the machines from stronger electromagnetic waves.

"A train will generate a lot of current and voltage, and as a result, the electromagnetic field generated will also be high," he said.

"But originally, we have not designed [our hospitals] for that … we made the room just for the MRI machine.

"When you're designing, you do not think there'll be [train] projects 50 or 100 years down the line."

While Dr Wanasinghe said it was not impossible to bolster existing Faraday cages, he said it would be expensive.

With additional expenses accrued from moving some of the Parkville medical equipment to East Melbourne, the government has been hesitant to outline specific details moving forward.

Health Minister Mary-Anne Thomas said it was "too early to definitively answer" whether the machines would be moved back to their original locations.

Artificial intelligence platforms

sdecoret - stock.adobe.com

Nvidia launches NIM Agent Blueprints to speed AI use

Nvidia introduced new microservice that helps enterprise developers deploy genai applications. it also introduced three blueprints for different use cases..

Esther Ajao, News Writer

AI hardware and software vendor Nvidia Corp. launched a new NIM microservices on Tuesday that aim to speed up AI app development.

NIM Agent Blueprints is a catalog of pre-trained, customizable AI workflows that enterprise developers can use to build and deploy generative AI applications.

The first three NIM Agent Blueprints introduced are digital humans , or avatars for customer service; multimodal PDF Data Extraction for Enterprise Retrieval Augmented Generation; and Generative Virtual Screening for Drug Discovery.

NIM Agent Blueprints give developers a head start when creating applications with AI agents , Nvidia said.

Blueprints include sample applications built with Nvidia NeMo , Nvidia NIM, and partner microservices.

NIM Agent Blueprints follow a GenAI market trend where many enterprises seek to move from ideation to implementation.

Solving a GenAI problem

Despite being in the age of implementation of generative AI, enterprises are still dealing with challenges that keep them from being successful with their deployments of GenAI systems.

Thus, Nvidia NIM attempts to solve some of the problems enterprises face implementing GenAI technology , including the speed at which enterprises integrate GenAI workflows, said Chirag Dekate, an analyst with Gartner.

"It's about creating pluggable, modular components that enterprises can build off," Dekate added.

While Nvidia could have chosen to give developers AI tools to build their applications, with NIMs such as NIM Agent Blueprints, the vendor provides enterprises with pretrained models that allow them to move quicker in building generative AI products and services, Futurum Group analyst Olivier Blanchard said.

While this is cost-effective, it might not be what every enterprise needs, Blanchard said.

"For enterprises that are super unique, NIM might not be the model," he said. "They might start somewhere else first and then use them to build additional layers of capabilities or features on top of their other product."

What Nvidia is providing is not unique to GenAI technology, said Rob Enderle, an analyst with Enderle Group.

"Part of what's required to be successful in the market, you have to have a complete solution, not just the technology," Enderle said. "Initially, generative AI was a technology. What Nvidia is doing is turning it into a complete solution."

Nvidia is not the only vendor endeavoring to make generative AI more than just a technology.

AMD, a competitor to Nvidia, is one of the leading companies in the movement, Enderle said.

The vendor last week purchased ZT Systems along with several other companies, including Mipsology , an AI software startup in France, to help with AI inference capabilities.

Google, AWS and Microsoft also are building tools to help enterprises easily deploy GenAI systems.

Nvidia software services

NIM Agent Blueprints allows Nvidia to beef up its software services, making services such as NIMs available regardless of the cloud provider.

It's about creating pluggable, modular components that enterprises can build off. Chirag Dekate Analyst, Gartner

"This is part of the strategic plan that Nvidia is executing to essentially create a vertically integrated alternative no matter where customers are building their solutions at scale," Dekate said. "By enabling these building blocks, like NIM Blueprints, what Nvidia is essentially embedding is higher-level modular architectures that basically pull through the Nvidia stack no matter where you run them."

On Monday, Nvidia also introduced new CUDA libraries, including new LLM applications.

New LLM applications in CUDA include NeMo Curator and SDG, or synthetic data generation.

NeMo Curator is an application that helps developers create custom datasets in LLM use cases.

Synthetic data generation is an LLM application that augments existing datasets with synthetic data to fine-tune models and LLM applications.

Esther Ajao is a TechTarget Editorial news writer and podcast host covering artificial intelligence software and systems.

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Speed, Distance and Time
Speed, Distance and Time
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Speed, Distance and Time
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COMMENTS

Problems on Trains
Try solving the sample questions given below based on Train problems and practise more to score more in the upcoming Government exams. Q 1. A train running at the speed of 56 km/hr crosses a pole in 18 seconds. What is the length of the train? 200m; 250m; 325m; 280m; 140m; Answer: (4) 280m. Solution: Speed = {56 × (5/18)} m/sec = (140/9) m/sec
Speed of Train
A train is running at a speed of 90 km/hr. if it crosses a pole in just 10 second, what is the length of the train? Solution: Speed of the train = 90 km/hr. Speed of the train = 90 × 5/18 m/sec = 25 m/sec. Time taken by the train to cross the pole = 10 seconds. Therefore, length of the train = 25 m/sec × 10 sec = 250 m. 4.
Algebra: Speed and Distance Problems
Solution: Two trains means two distance formulas: D A = r A · t A and D B = r B · t B. Your first goal is to plug in any values you can determine from the problem. Since Train A travels 95 mph, r A = 95; similarly, r B = 110. Notice that the problem also says that the trains leave at the same time. This means that their travel times match ...
Problems on Trains
Problems on Trains, like concepts of speed, distance, and time, focus on evaluating a train's speed, distance traveled, and time spent under various conditions. ... Tips & Tricks for Solving Train Problems. To help hopefuls prepare for and conquer the quantitative aptitude section, here are a few pointers that will help you solve train problems ...
Train Problems: Concepts, Examples and Practice Questions
Train Problems form an interesting portion of the time-distance problems. The Train Problems are a bit different than the regular problems on the motion of the objects. ... We have the speed of the train = 60 km/hr or 60×(5/18) = 50/3 m/s. ... How can u solve ex 4. Reply. Rinku Uppal says: June 25, 2019 at 6:50 am. Many of your questions are ...
PROBLEMS ON TRAINS WITH SOLUTIONS
Solution : speed = 20 m/sec. To convert m/sec to km/h, multiply the given m/sec by 18/5. = 20 x 18/5 km/hr. = 72 km/hr. Problem 2 : The length of a train is 300 meter and length of the platform is 500 meter. If the speed of the train is 20 m/sec, find the time taken by the train to cross the platform.
PDF Speed, Time, and Distance Problems
now solve these types of problems with your knowledge of systems of equations. One of the most effective ways to do so is to first build a chart. Example 1. A train leaves a station at 9:00 AM and travels with a constant speed of 90 km/h. Another train leaves the same station 10 minutes later, traveling to the same direction at the speed of 100 ...
Math Practice Problems
Train Problems - Sample Math Practice Problems The math problems below can be generated by MathScore.com, a math practice program for schools and individual families. ... Solve. If asked for time, a proper answer looks like this: 1:35am. 1. A train leaves Venice at 7:00 pm, averaging 80 mph.
Problems on Trains
Time required = Distance / Speed. In the provided example, distance is just the length of the trains, and speed is determined by the relative speed. Because both trains are heading in opposing directions, we must add their speeds. ⇒ Time taken = (500m+300m)/ (20+30) ⇒ Time Taken = 800/50. ⇒ 16 Seconds.
3 (& Half) Concepts for Solving Speed Train Problems with Length
Mayank explains 3 key concepts for solving all problems involving trains, platforms, bridges and poles.Speed Problems with Length of Objects @0:07Trains Appr...
Velocity and Speed: Problems with Solutions
Solution to Problem 4. Problem 5: If I can walk at an average speed of 5 km/h, how many miles I can walk in two hours? Solution to Problem 5. Problem 6: A train travels along a straight line at a constant speed of 60 mi/h for a distance d and then another distance equal to 2d in the same direction at a constant speed of 80 mi/h.
Two trains leaving the station at different times...
In this problem, we know that one train starts two hours before the other one and travels at a known rate. ... Now both trains are moving, one traveling at 60 mi/hr and the other at 70 mi/hr. Their closing speed is just 60 + 70 = 130 mi/hr, and the total distance to go is 335 mi. Solve the rate equation for t to get t = d/r. ... so your next ...
Problems on Trains
The speed of the train is: 3. The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is: 4. Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 23 seconds.
Velocity and Speed: Solutions to Problems
Problem 5: If I can walk at an average speed of 5 km/h, how many miles I can walk in two hours? Solution to Problem 5: distance = (average speed) * (time) = 5 km/h * 2 hours = 10 km using the rate of conversion 0.62 miles per km, the distance in miles is given by distance = 10 km * 0.62 miles/km = 6.2 miles Problem 6: A train travels along a straight line at a constant speed of 60 mi/h for a ...
Train Problems, Check Example, Formulas, Shortcuts
Distance = Speed * Time. For example, if a train is traveling at a speed of 80 km/hr and it takes 3 hours to reach its destination, we can calculate the distance covered as follows: Distance = 80 km/hr * 3 hours = 240 km. Average Speed Problems Calculating the average speed of a train over a certain distance is another common type of problem on ...
Problems on Trains: Speed, Time, Distance, Formula, Examples
Ans: Let us say the length of the trains is x m, and the distance covered by it is ( x + x) = 2 x m. The relative speed of the trains = ( 40 - 30) kmph = 10 kmph = 10 × 5 18 = 25 9 m / sec. Speed of the faster train = 2 x 36. So, 2 x 36 = 25 9. or, x = 25 × 36 18 = 50 m. Hence, the length of each train is 50 m. Q.4.
Problem on Trains MCQ [Free PDF]
Speed of trains are 80 km/hr and 100 km/hr and lower speed train start 1 hour earlier. FORMULA USED: Distance = Time × Speed. CALCULATION: Speed of trains are 80 km/hr and 100 km/hr and slower speed train start 1 hour earlier. Distance covered by slower train in 1 hour = 80 × 1 = 80 km. Relative speed = 100 - 80 = 20 km/hr
Problems on Trains
Solution: To calculate the distance here you need to add the distance traveled by both the trains together. Distance traveled by train A will be: d= s t, the rate at which it travels here is 50mph and the time is 2 hours. So the distance traveled by train A will be 50×2 = 100. Similarly, distance traveled by train B will be 70×2 = 140.
Problems on Trains
Find the distance between Delhi and Pune. Solution: Let t be the time after they meet. Distance 1 = Speed * Time = 80 * t = 80t. Distance 2 = Speed * Time = 95 * t = 95t. As the distance gap between both trains is 180 kms. Therefore, we can say that: 95t - 80t = 180. 15t = 180.
Classic Two Trains Meeting Problem
More information at: http://firesciencetools.com/The classic two trains moving at constant velocity heading toward each other, when and where will they meet ...
Problems on Trains Formulas and Sample Questions with Solutions
Problems on train formulas are important to solve the train problems quickly. In this blog, you can learn train problem formula and tricks to solve problems on trains. ... (As speed): (B's speed) = Problem on trains with solutions - Train problems with solutions: Let's have some solved examples to understand the topic clearly. Ex.1. A ...
MathScore Practice: Train Problems
Mastery. Solve. If asked for time, a proper answer looks like this: 1:35am. 1. A train leaves Kansas City for a nearby city at 9:30 am, averaging 35 mph. Another train leaves the nearby city for Kansas City at 10:15 am, averaging 55 mph. If the nearby city is 431.25 miles from Kansas City, to the nearest minute, at what time will the two trains ...
Facing the Problems on Train
As train problems are an extension of the topic: of speed, distance, and time, the basic formulas that are used for solving questions on a train are: Speed = Distance/Time. Distance = Speed * Time. Time = Distance/Speed. There is a lot variety of questions on trains. Basic problems involving the above three formulas are common, but the range of ...
Solving the Elusive Baseband to Antenna Problem using RFDAC Technology
Larry Welch is a Senior Applications Engineer in the High Speed Converter Group at Analog Devices, Inc. (Wilmington, MA). He joined ADI in 1996 and has held a variety of systems engineering and applications engineering roles in wired communications, wireless communications and high speed data converter groups.
HS2 trains too high for station platforms
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The issue is one explored in 2020 by the California High Speed Rail Authority, who investigated the impacts of electromagnetic interference from trains on a planned project from Burbank to Los ...
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AI hardware and software vendor Nvidia Corp. launched a new NIM microservices on Tuesday that aim to speed up AI app development. NIM Agent Blueprints is a catalog of pre-trained, customizable AI workflows that enterprise developers can use to build and deploy generative AI applications. ... Solving a GenAI problem. Despite being in the age of ...

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