FIND THE TIME TAKEN BY A TRAIN TO PASS A MAN

Time taken by a train of length l meters to pass a pole or standing man or signal post is equal to the time taken by the train to cover l meters.

The relationship between distance, speed and time.

Time  =  Distance / Speed 

Speed  =  Distance / Time

Distance  =  Time ⋅ Speed

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.

Example 1 :

A train 100 m long is running at the speed of 30 km/hr. Find the time taken by it to pass a man standing near the railway line.

Solution :

Length of the train  =  100 m

Speed  =  30 km/hr

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

  =  30 ⋅ (5/18)

  =  5 ⋅ (5/3)

Required speed  =  (25/3) m/sec

Time taken by a train of length l meters to pass a pole or standing man or signal post is equal to the time taken by the train to cover l meters.

Time  =  distance / speed

  =  100 / (25/3)

  =  12 seconds.

So, the train of length 100 m is taking 12 seconds to cross a man standing near the railway line.

Example 2 :

In what time will a train 100 meters long cross an electric pole, if the speed be 144 km/hr.

Solution :

Length of the train  =  100 meters

Speed of the train  =  144 km/hr

Speed in m/sec  =  144 ⋅ (5/18)

  =  8 ⋅ 5

  =  40 m/sec

Time  =  Distance / Speed

=  100/40

=  2.5 seconds

So, the train of length 100 m crosses an electric pole in 2.5 seconds.

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