TRAIN PASSES A MOVING OBJECT IN THE SAME DIRECTION

If two trains or two bodies are moving in the same direction at u m/s and v m/s, then their

R elative Speed   =  (u  - v)  m / s

Distance covered  =  Sum of length of two trains

Time  =  Distance / Speed

Time  =  Sum of length of two trains / (u - v)

To convert minutes into hour, we should divide the given minutes by 60.

• If we want to convert the speed from km/hr to m/sec, we should multiply the speed by 5/18.
• If we want to convert the speed from m/sec to km/hr, we should multiply the speed by 18/5.

Solved Examples

Example 1 :

A train 150 m long is running with a speed of 68 kmph. In what time will it pass a man who is running at 8 kmph in the same direction in which the train is going ?

Solution :

The train and a man are travelling in the same direction.

So,

Relative speed  =  Speed of the train - Speed of the man

  =  68 - 8

  =  60 km/hr

Converting the speed from km/hr to m/sec

  =  60 ⋅ (5/18)

  =  50/3

Since the train crosses the man, the distance covered by the train is 150 m (the length of the train).

Time  =  150 / (50/3)

  =  150 ⋅ (3/50)

  =  9 seconds

Example 2 :

Two trains 100 meters and 120 meters long are running in the same direction with speeds of 72 km/hr and 54 km/hr. In how much time will the first train cross the second ?

Solution :

Since both are moving objects and the total distance covered

  =  100 + 120

  =  220 meters

Relative speed  =  72 - 54

=  18

Relative speed in m/sec  =  18 ⋅ (5/18)

=  5 m/sec

Time  =  Distance / Speed

=  220 / 5

  =  44 seconds

Hence the first train is taking 44 seconds to cross the second train.

Example 3 :

A train running at 54 kmph takes 20 seconds to pass a platform. Next it takes 12 seconds to pass a man walking at 6 kmph in the same direction in which the train is going. Find the length of the train and length of the platform.

Solution :

Let x and y be the length of the train and length of platform.

Distance covered by the train while crossing the platform

  =  x + y

Time taken by the train to cross the platform  =  20 sec

Speed of the train  and =  54 km/hr

54 km/hr  =  54 ⋅ (5/18)

  =  15 m/sec

Time taken by the train to cross the platform is 

Time  =  Distance / Speed

20  =  (x + y) / 15 -----(1)

Time taken by the train to cross the platform  =  12 sec

Speed of the man  =  6 km/hr

Relative speed  =  54 - 6

  =  48 kmph

48 km/hr  =  48 ⋅ (5/18)

  =  (40/3) m/sec

Time taken by the train to cross a man is 

Time  =  Distance / Speed

12  =  x / (40/3)

x  =  160

By applying the value of x in (1), we get

20  =  (160 + y) / 15

y  =  300 - 160

y  =  140 m

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

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