PROBLEMS ON TRAINS WITH SOLUTIONS - 2

Problem 1 :

A trains covers 240 kilometers in 4 hours. Find the speed of the train in meter per second.  

Solution :

Speed  =  Distance/Time

Speed  =  240/4 kmph

Speed  =  60 kmph

Speed  =  60 ⋅ 5/18 m/sec

Speed  =  16.67 m/sec

Hence, the speed of the train is 16.67 m/sec. 

Problem 2 :

A train of length 250 meters is running at a speed of 90 kmph. Find the time taken by the train to cross a pole. 

Solution :

The length of the train is given meters.

So, let us convert the speed of the train from kmph to meter per second (m/sec).

Speed  =  90 kmph 

Speed  =  90 ⋅ 5/18 m/sec

Speed  =  25 m/sec

Distance need to be covered to cross the pole is

=  Length of the train

So, distance traveled by the train to cross the pole is 

=  250 meters

Time taken by the train to cross the pole is

=  Distance/Speed 

=  250 / 25

=  10 seconds

Hence, time taken by the train to cross the pole is 40 seconds.

Problem 3 :

Two trains of length  250m and 200m run on parallel lines. When they run in the same direction, it will take 30 second to cross each other. When they run in opposite direction, it will take 10 seconds to cross each other. Find the speeds of the two trains (in kmph).   

Solution :

Let the speeds of the two trains be S₁ and S₂ 

In same direction or opposite directions, the total distance covered by the two trains to cross each other is equal to sum of the lengths of the two trains.

So, the total distance covered by the two trains to cross each other is

=  250 + 200  

=  450 m

When they run in same direction direction, the relative speed is

S₁ - S₂  =  450 /30

S₁ - S₂  =  15 -------(1)

When they run in same direction direction, the relative speed is

S₁ + S₂  =  450 /10

S₁ + S₂  =  45 -------(2)

Solving the (1) and (2), we get 

S₁  =  30 m/sec  =  30 ⋅ 18/5 kmph  =  108 kmph 

S₂  =  15 m/sec  =  15 ⋅ 18/5 kmph  =  54 kmph 

Hence, speeds of the two trains are 108 kmph and 54 kmph.

Problem 4 :

Find the time taken by a train 100m long running at a speed of 60 kmph to cross another train of length 80 m running at a speed of 48 kmph in the same direction.  

Solution :

In same direction or opposite directions, the total distance covered by the two trains to cross each other is equal to sum of the lengths of the two trains.

So, the total distance covered by the two trains to cross each other is

=  100 + 80  

=  180 m 

When the trains run in same direction direction, the relative speed is

 =  60 - 48  

=  12 kmph

=  12 ⋅ 5/18

=  10/3 m/sec 

Time taken by the two trains to cross each other is

=  Distance/Speed

=  180 / (10/3) seconds 

=  180 ⋅ 3/10 seconds 

=  54 seconds 

Hence, time taken by the faster train to cross the slower train is 54 seconds.

Problem 5 :

Two trains of equal length are running on parallel lines in the same direction at 46 kmph and 36 kmph. The faster train crosses the slower train in 36 seconds. Find the length of each train.   

Solution :

Let "x" be the length of each train 

Sum of the lengths of the two trains is

=  x + x

=  2x

When the trains run in same direction direction, the relative speed is

=  46 - 36

=  10 kmph

=  10 ⋅ 5/18 m/sec

=  25/9 m/sec 

We know the fact that when two trains run in the same direction, the distance covered by each train is equal to sum of the lengths of the two trains. 

So, the distance covered by the faster train is 

=  2x

Given : The faster train crosses the slower train in 36 seconds.

So, the faster train takes 36 seconds to cover the distance 2x. 

Then, we have

Distance  =  Speed ⋅ Time 

2x  =  25/9 ⋅ 36  

2x  =  100 

x  =  50  

Hence, the length of each train is 50 meters. 

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