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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72 km/hr in m/s = 72*5/18 = 20 m/s now total distance = 110+132 m = 242 m
so,time = 242/20 = 12.1 seconds
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