Relative Speed And Train Questions

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RELATIVE SPEEED AND TRAIN QUESTIONS


Speed has no sense of direction unlike the velocity. Relative speed is the speed of one object as observed from another moving object. Questions on train are the classic examples of relative speed and in all these questions it is assumed that trains move parallel to each other – whether in the same direction or the opposite direction. Thus, we shall see how the relative speed is calculated and using it we come to know the time taken by the trains to cross each other and some other like aspects.


Important Formulas – Problems on Trains

  1. x km/hr = (x×5)/18 m/s 

 

  1. y m/s = (y×18)/5 km/hr 

 

  1. Speed = distance/time, that is, s = d/t

 

  1. velocity = displacement/time, that is, v = d/t

 

  1. Time taken by a train x meters long to pass a pole or standing man or a post 
    = Time taken by the train to travel x meters.

 

  1. Time taken by a train x meters long to pass an object of length y meters

= Time taken by the train to travel (x + y) metres.

 

  1. Suppose two trains or two objects are moving in the same direction at v1 m/s and v2 m/s where v1 > v2,

then their relative speed = (v1 – v2) m/s

 

  1. Suppose two trains or two objects are moving in opposite directions at v1 m/s and v2 m/s ,

then their relative speed = (v1+ v2) m/s

 

  1. Assume two trains of length x metres and y metres are moving in opposite directions at v1 m/s and v2 m/s, Then

The time taken by the trains to cross each other = (x+y) / (v1+v2) seconds

 

  1. Assume two trains of length x metres and y metres are moving in the same direction at at v1 m/s and v2 m/s where v1 > v2, Then

The time taken by the faster train to cross the slower train = (x+y) / (v1-v2) seconds

 

  1. Assume that two trains (objects) start from two points P and Q towards each other at the same time and after crossing they take p and q seconds to reach Q and P respectively. Then,

A’s speed: B’s speed = √q: √p

 

Solved Examples

Level 1

1. A train is running at a speed of 40 km/hr and it crosses a post in 18 seconds. What is the length of the train?

A. 190 metres

B. 160 metres

C. 200 metres

Answer : Option C

D. 120 metres

Explanation :

Speed of the train, v = 40 km/hr = 40000/3600 m/s = 400/36 m/s 

Time taken to cross, t = 18 s 

Distance Covered, d = vt = (400/36)× 18 = 200 m 

Distance covered is equal to the length of the train = 200 m

2. A train having a length of 240 m passes a post in 24 seconds. How long will it take to pass a platform having a length of 650 m?

A. 120 sec

B. 99 s

C. 89 s

D. 80 s

Answer : Option C

Explanation :

v = 240/24 (where v is the speed of the train) = 10 m/s

t = (240+650)/10 = 89 seconds

3.Two trains having length of 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions (on parallel tracks). The time which they take to cross each other, is

A. 10.8 s

B. 12 s

C. 9.8 s

D. 8 s

Answer : Option A

Explanation :

Distance = 140+160 = 300 m

Relative speed = 60+40 = 100 km/hr = (100×10)/36 m/s 

Time = distance/speed = 300 / (100×10)/36 = 300×36 / 1000 = 3×36/10 = 10.8 s

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

A. 79.2 km/hr

B. 69 km/hr

C. 74 km/hr

D. 61 km/hr

Answer : Option A

Explanation :

Let x is the length of the train and v is the speed

Time taken to move the post = 8 s 

=> x/v = 8 

=> x = 8v — (1)

Time taken to cross the platform 264 m long = 20 s

(x+264)/v = 20

=> x + 264 = 20v —(2)

Substituting equation 1 in equation 2, we get

8v +264 = 20v

=> v = 264/12 = 22 m/s

= 22×36/10 km/hr = 79.2 km/hr

5. Two trains, one from P to Q and the other from Q to P, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is

A. 2 : 3

B. 2 :1

C. 4 : 3

D. 3 : 2

Answer : Option C

Explanation :

Ratio of their speeds = Speed of first train : Speed of second train

= √16: √ 9

= 4:3

 6. Train having a length of 270 meter is running at the speed of 120 kmph . It crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?

A. 320 m

B. 190 m

C. 210 m

D. 230 m

Answer : Option D

Explanation :

Relative speed = 120+80 = 200 kmph = 200×10/36 m/s = 500/9 m/s

time = 9s

Total distance covered = 270 + x where x is the length of other train

(270+x)/9 = 500/9

=> 270+x = 500

=> x = 500-270 = 230 meter

7. Two stations P and Q are 110 km apart on a straight track. One train starts from P at 7 a.m. and travels towards Q at 20 kmph. Another train starts from Q at 8 a.m. and travels towards P at a speed of 25 kmph. At what time will they meet?

A. 10.30 a.m

B. 10 a.m.

C. 9.10 a.m.

D. 11 a.m.

Answer : Option B

Explanation :

Assume both trains meet after x hours after 7 am

Distance covered by train starting from P in x hours = 20x km

Distance covered by train starting from Q in (x-1) hours = 25(x-1)

Total distance = 110

=> 20x + 25(x-1) = 110

=> 45x = 135

=> x= 3 Means, they meet after 3 hours after 7 am, ie, they meet at 10 am

8. Two trains are running in opposite directions in the same speed. The length of each train is 120 meter. If they cross each other in 12 seconds, the speed of each train (in km/hr) is

A. 42

B. 36

C. 28

D. 20

Answer : Option B

Explanation :

Distance covered = 120+120 = 240 m

Time = 12 s

Let the speed of each train = v. Then relative speed = v+v = 2v

2v = distance/time = 240/12 = 20 m/s

Speed of each train = v = 20/2 = 10 m/s 

= 10×36/10 km/hr = 36 km/hr

 

Level 2

1.  A train, 130 meters long travels at a speed of 45 km/hr crosses a bridge in 30 seconds. The length of the bridge is

A. 270 m

B. 245 m

C. 235 m

D. 220 m

Answer : Option B

Explanation :

Assume the length of the bridge = x meter

Total distance covered = 130+x meter

total time taken = 30s

speed = Total distance covered /total time taken = (130+x)/30 m/s

=> 45 × (10/36) = (130+x)/30

=> 45 × 10 × 30 /36 = 130+x

=> 45 × 10 × 10 / 12 = 130+x

=> 15 × 10 × 10 / 4 = 130+x

=> 15 × 25 = 130+x = 375

=> x = 375-130 =245

2. A train has a length of 150 meters. It is passing a man who is moving at 2 km/hr in the same direction of the train, in 3 seconds. Find out the speed of the train.

A. 182 km/hr

B. 180 km/hr

C. 152 km/hr

D. 169 km/hr

Answer : Option A

Explanation :

Length of the train, l = 150m 

Speed of the man, Vm= 2 km/hr 

Relative speed, Vr = total distance/time = (150/3) m/s = (150/3) × (18/5) = 180 km/hr 

Relative Speed = Speed of train, Vt – Speed of man (As both are moving in the same direction) 

=> 180 = Vt – 2  => Vt = 180 + 2 = 182 km/hr

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

A. Insufficient data

B. 3 : 1

C. 1 : 3

D. 3 : 2

Answer : Option D

Explanation :

Let the speed of the trains be x and y respectively 

length of train1 = 27x

length of train2 = 17y

Relative speed= x+ y

Time taken to cross each other = 23 s

=> (27x + 17 y)/(x+y) = 23 => (27x + 17 y)/ = 23(x+y)

=> 4x = 6y => x/y = 6/4 = 3/2

4. A jogger is running at 9 kmph alongside a railway track in 240 meters ahead of the engine of a 120 meters long train . The train is running at 45 kmph in the same direction. How much time does it take for the train to pass the jogger?

A. 46

B. 36

C. 18

D. 22

Answer : Option B

Explanation :

Distance to be covered = 240+ 120 = 360 m

Relative speed = 36 km/hr = 36×10/36 = 10 m/s

Time = distance/speed = 360/10 = 36 seconds

5. A train passes a platform in 36 seconds. The same train passes a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, The length of the platform is

A. None of these

B. 280 meter

C. 240 meter

D. 200 meter

Answer : Option C

Explanation :

Speed of the train = 54 km/hr = (54×10)/36 m/s = 15 m/s

Length of the train = speed × time taken to cross the man = 15×20 = 300 m

Let the length of the platform = L

Time taken to cross the platform = (300+L)/15 

=> (300+L)/15 = 36

=> 300+L = 15×36 = 540 => L = 540-300 = 240 meter

6. A train overtakes two persons who are walking in the same direction to that of the train at 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively. What is the length of the train?

A. 62 m

B. 54 m

C. 50 m

D. 55 m

Answer : Option C

Explanation :

Let x is the length of the train in meter and v is its speed in kmph

x/9 = (v-2) (10/36) — (1)

x/10 = (v-4) (10/36) — (2)

Dividing equation 1 with equation 2

10/9 = (v-2)/(v-4) => 10v – 40 = 9v – 18 => v = 22

Substituting in equation 1, x/9 = 200/36  => x = 9×200/36 = 50 m

7. A train is traveling at 48 kmph. It crosses another train having half of its length, traveling in opposite direction at 42 kmph, in 12 seconds. It also passes a railway platform in 45 seconds. What is the length of the platform?

A. 500 m

B. 360 m

C. 480 m

D. 400 m

Answer : Option D

Explanation :

Speed of train1 = 48 kmph

Let the length of train1 = 2x meter

Speed of train2 = 42 kmph

Length of train 2 = x meter (because it is half of train1’s length)

Distance = 2x + x = 3x

Relative speed= 48+42 = 90 kmph = 90×10/36 m/s = 25 m/s

Time = 12 s

Distance/time = speed => 3x/12 = 25 

=> x = 25×12/3 = 100 meter

Length of the first train = 2x = 200 meter

Time taken to cross the platform= 45 s

Speed of train1 = 48 kmph = 480/36 = 40/3 m/s

Distance = 200 + y where y is the length of the platform

=> 200 + y = 45×40/3 = 600

=> y = 400 meter

8. A train, 800 meter long is running with a speed of 78 km/hr. It crosses a tunnel in 1 minute. What is the length of the tunnel (in meters)?

A. 440 m

B. 500 m

C. 260 m

D. 430 m

Answer : Option B

Explanation :

Distance = 800+x meter where x is the length of the tunnel

Time = 1 minute = 60 seconds

Speed = 78 km/hr = 78×10/36 m/s = 130/6 = 65/3 m/s

Distance/time = speed

(800+x)/60 = 65/3 => 800+x = 20×65 = 1300

=> x = 1300 – 800 = 500 meter

9. Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. If the fast train completely passes a man sitting in the slower train in 5 seconds, the length of the fast train is :

A. 19 m

B. 2779 m

C. 1329 m

D. 33 m

Answer : Option B

Explanation :

Relative speed = 40-20 = 20 km/hr = 200/36 m/s = 100/18 m/s

Time = 5 s

Distance = speed × time = (100/18) × 5 = 500/18 m = 250/9 = 2779 m = length of the fast train

 

 

 

 

 

 

 

 

 

 

 

 

 


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Relative speed is the speed of one object relative to another. It is calculated by subtracting the speeds of the two objects. For example, if a train is moving at 100 miles per hour and another train is moving at 50 miles per hour, the relative speed of the two trains is 50 miles per hour.

Train questions are a type of math problem that involves calculating the speed, distance, or time of a train. They can be challenging, but they can also be fun to solve. There are many different types of train questions, but some of the most common include:

Train problems are a type of physics problem that involves calculating the forces and energy of a train. They can be challenging, but they can also be fun to solve. There are many different types of train problems, but some of the most common include:

Train chasing, overtaking, crossing, and meeting are all examples of relative speed problems. In each of these problems, there are two trains moving at different speeds. The question is how long it will take for one train to catch up to, overtake, cross, or meet the other train.

To solve a relative speed problem, you need to know the speeds of the two trains and the distance between them. You can then use the following formula to calculate the time it will take for one train to catch up to, overtake, cross, or meet the other train:

Time = Distance / Relative Speed

For example, if one train is moving at 100 miles per hour and another train is moving at 50 miles per hour, and the distance between them is 100 miles, it will take 2 hours for the first train to catch up to the second train.

Train questions and problems can be challenging, but they can also be fun to solve. With a little practice, you can learn how to solve even the most difficult problems.

Here are some frequently asked questions and short answers about relative speed and train questions:

Sure, here are some MCQs without mentioning the topic Relative Speed And Train Questions:

  1. A car travels 100 miles in 2 hours. What is the Average speed of the car?
  2. A train travels 200 miles in 4 hours. What is the average speed of the train?
  3. A plane travels 300 miles in 1 hour. What is the average speed of the plane?
  4. A boat travels 400 miles in 2 hours. What is the average speed of the boat?

  5. A bicycle travels 500 miles in 5 hours. What is the average speed of the bicycle?

  6. A car travels 100 miles in 2 hours. If the car’s speed is constant, what is the car’s speed in miles per hour?

  7. A train travels 200 miles in 4 hours. If the train’s speed is constant, what is the train’s speed in miles per hour?
  8. A plane travels 300 miles in 1 hour. If the plane’s speed is constant, what is the plane’s speed in miles per hour?
  9. A boat travels 400 miles in 2 hours. If the boat’s speed is constant, what is the boat’s speed in miles per hour?

  10. A bicycle travels 500 miles in 5 hours. If the bicycle’s speed is constant, what is the bicycle’s speed in miles per hour?

  11. A car travels 100 miles in 2 hours. If the car’s speed is increasing, what is the car’s speed at the end of the first hour?

  12. A train travels 200 miles in 4 hours. If the train’s speed is increasing, what is the train’s speed at the end of the first hour?
  13. A plane travels 300 miles in 1 hour. If the plane’s speed is increasing, what is the plane’s speed at the end of the first half hour?
  14. A boat travels 400 miles in 2 hours. If the boat’s speed is increasing, what is the boat’s speed at the end of the first hour?

  15. A bicycle travels 500 miles in 5 hours. If the bicycle’s speed is increasing, what is the bicycle’s speed at the end of the first hour?

  16. A car travels 100 miles in 2 hours. If the car’s speed is decreasing, what is the car’s speed at the end of the first hour?

  17. A train travels 200 miles in 4 hours. If the train’s speed is decreasing, what is the train’s speed at the end of the first hour?
  18. A plane travels 300 miles in 1 hour. If the plane’s speed is decreasing, what is the plane’s speed at the end of the first half hour?
  19. A boat travels 400 miles in 2 hours. If the boat’s speed is decreasing, what is the boat’s speed at the end of the first hour?
  20. A bicycle travels 500 miles in 5 hours. If the bicycle’s speed is decreasing, what is the bicycle’s speed at the end of the first hour?

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