FIND THE TIME TAKEN BY A TRAIN TO CROSS A BRIDGE OR TUNNEL

Time taken by a train of length l meters to pass a standing object of length b meters is the time taken by the train to cover (l + b) 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 is moving at a speed of 132 km/hr. If the length of the train is 110 meters, how long will it take to cross a railway platform 165 meters long.

Solution :

Standing object is railway platform of length 165 meters.

Moving object is train of length 110 meters and running at the speed of 132 km/hr.

Converting the speed from km/hr to m/sec

  =  132 ⋅ (5/18)

  =  22 ⋅ (5/3)

  =  (110/3) m/sec

Distance to be covered  =  110 + 165

=  275 m

Time  =  distance / speed

  =  275 / (110/3)

  =  275 ⋅ (3/110)

  =  7.5 seconds

So, the train of length 100 m long is taking 7.5 seconds to cross the railway platform 165 meters long.

Example 2 : 

How long does a train 110 meters long running at the speed of 72 km/hr take to cross a bridge 132 meters in length ?

Solution :

Standing object is bridge of length 132 meters.

Moving object is train of length 110 meters.

Distance to be covered  =  132 + 110

  =  242 meters

Speed of the train  =  72 km/hr

Speed in m/sec  =  72 ⋅ (5/18)

=  20 m/sec

Time  =  Distance / Speed

=  242 / 20

=  12.1 seconds 

So, the train of length 132 m is taking 12.1 seconds crosses the bridge of length 110 m. 

Example 3 :

A man is standing on a railway bridge which is 180 m long. He finds that a train crosses the bridge in 20 seconds but himself in 8 seconds. Find the length of the train and its speed.

Solution :

Let l and x be the length and speed of the train respectively.

The train of length l meters crosses a railway bridge of length 180 m in 20 seconds.

Time  =  Distance / Speed

20  =  (l + 180) / x

x  =  (l + 180)/20 -----(1)

The train of length l meters crosses a man in 8 seconds.

8  =  l / x

x  =  l / 8 -----(2)

(1)  =  (2)

(l + 180)/20  =  l  / 8

8(l + 180)  =  20l

20l - 8l  =  1440

12l  =  1440

l  =  1440/12 

l  =  120

By applying the value of l in (2), we get

x  =  120/8

x  =  15 m/sec

x  =  15 (18/5)

x  =  54 km/hr

Hence the length of the train is 120 m and speed is 54 km/hr.

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