Question
A freight train requires 17.6 seconds to pass a
stationary person and 28 seconds to traverse a 260-meter-long tunnel. Simultaneously, a motorcycle can cross a 315-meter-long bridge in 15 seconds. Determine the time needed for the train to entirely overtake the bike.Solution
ATQ, Let the length of the freight trains = 'l' meters Then, distance travelled by the freight trains in 17.6 seconds = 'l' meters Distance travelled by the Freight train in 28 seconds = (l + 260) meters So, distance travelled by the freight train in (28 - 17.6) seconds = l + 260 - l = 260 meters So, speed of the Freight train = 260 ÷ 10.4 = 25 m/s And so, length of the freight train = 25 × 17.6 = 440 meters Speed of the bike = 315 ÷ 15 = 21 m/s So, relative speed of the freight train w.r.t to the bike = 25 - 21 = 4 m/s And so, time taken by the freight train to completely overtake the bike = 440 ÷ 4 = 110 seconds
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