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A 450 m long train crosses a man walking at a speed of 6 km/h in the same direction in 54 seconds. What is the speed (in km/h) of the train?
30 km/h
36 km/h
40 km/h
32 km/h
36 km/h
Use the conversion factor 18/5 to transform m/s to km/h quickly. Since distance is 450m and time is 54s, SrelтАЛ=450/54=25/3 m/s. Multiply by 18/5 to get 30 km/h, then add the man's speed 6 km/h.
Length of train = 450 m, Speed of man = 6 km/h, Time taken = 54 seconds.
SrelтАЛ=TimeDistanceтАЛ,VtrainтАЛтИТVmanтАЛ=SrelтАЛ
Use the conversion factor 18/5 to transform m/s to km/h quickly. Since distance is 450m and time is 54s, SrelтАЛ=450/54=25/3 m/s. Multiply by 18/5 to get 30 km/h, then add the man's speed 6 km/h.
Students often forget that the relative speed is the difference between train speed and man's speed when moving in the same direction, or they fail to convert units correctly.
Calculate relative speed in m/s
Since the train covers its own length to cross the man, the relative speed is distance divided by time.
SrelтАЛ=54450тАЛ=325тАЛ┬аm/s
Convert relative speed to km/h
Convert the speed from m/s to km/h by multiplying by 518тАЛ.
SrelтАЛ=325тАЛ├Ч518тАЛ=30┬аkm/h
Find the speed of the train
In the same direction, relative speed is the difference of the two speeds. Let VTтАЛ be the speed of the train.
VTтАЛтИТ6=30тЯ╣VTтАЛ=36┬аkm/h
B is correct because the calculated relative speed is 30 km/h, which implies the train's speed is 36 km/h after accounting for the man's speed.
This concept of relative speed is identical to calculating the closing speed of two vehicles in 'Boats and Streams' where speeds are added/subtracted based on direction.