When the train passes through a bridge or platform or tunnel or a stationary object having some length
If length of train = x meters and length of the stationery object = y meters.
Also, speed of the train is z km/hr, then time taken by the train to pass the stationary object having length y meters.
= (length of the train + length of stationary object)/speed of the train
= (x meters + y meters)/z km/hr
Note: Change km/hr to m/sec.
Solved examples to calculate when the train passes through a bridge or a stationary object having some length.
1. A train 175 m long crosses a bridge which is 125 m long in 80 seconds. What is the speed of the train?
Length of the train = 175 m.
Length of the bridge = 225 m
Distance covered by the train to cross the bridge = (175 + 225) m
= 400 m
Time taken by the train to cross the bridge = 80 seconds
Speed = distance/time
= 400/80 m/sec
= 5 m/sec.
2. A train 220 m long is running at a speed of 36 km/hr. What time will it take to cross a 110 m long tunnel?
Length of the train = 220 m
Length of the tunnel = 110 m
Therefore, length of the train + length of the tunnel = (220 + 110) m = 330m
Speed of the train = 36 km/hr
Speed of the train = 36 × 5/18 m/sec = 10 m/sec
Therefore, time taken by the train to cross the tunnel = 330 m/10 m/sec.
= 33 seconds.
3. Find the time taken by 150 m long train passes through a bridge which is 100 m long, running at a speed of 72 km/hr.
Speed of train = 72 km/hr = 72 × 5/18 m/sec = 20 m/sec
In order to cross a bridge of length 100 m, the train will have to cover a distance = (150 + 100) m = 250 m
Thus, speed = 20 m/sec and distance = 250 m
Time = distance/speed
= 250m/20 m/sec
= 25/2 sec
= 12.5 sec.
4. A 90 m long train is running at a speed of 54 km/hr. If it takes 30 seconds to cross a platform, find the length of the platform.
Speed of the train = 54 km/hr = 54 × 5/18 m/sec = 15 m/sec
Time taken to cross the bridge = 30 sec
Distance covered by train to cross the platform = speed × time
= (15 × 30) m
= 450 m
To cross the platform, train covers a distance = length of train + length of platform
450 m = 90 m + length of platform
Therefore, length of platform = (450 – 90) m = 360 m