Question
A train running at 54 km/h crosses a man running in the
same direction at 6 km/h in 18 seconds, and also crosses a bridge in 45 seconds. Find: (a) the length of the train, (b) the length of the bridge.Solution
Speeds in m/s: 54 km/h = 54×5/18 = 15 m/s 6 km/h = 6×5/18 = 5/3 m/s Relative speed (train w.r.t man, same direction): 15 − 5/3 = (45 − 5)/3 = 40/3 m/s (a) When crossing the man, distance covered = length of train = L Time = 18 s ⇒ L = (40/3) × 18 = 40 × 6 = 240 m (b) When crossing the bridge, distance = L + B Train speed = 15 m/s, time = 45 s: L + B = 15 × 45 = 675 So B = 675 − 240 = 435 m.
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