A train takes 10 seconds to pass a tree and 14 seconds to pass through a tunnel 112 meters long. A bike is moving in the same direction as the train at a speed of 33 m/s. How much time will the bike take to completely cross the train?

ATQ, Let the length of the train = ‘y’ metres Then, distance covered by the train in 10 seconds = ‘y’ metres Distance covered by the train in 14 seconds = (y + 112) metres So, distance covered by the train in (14 – 10) seconds = y + 112 – y = 112 metres So, speed of the train = (112/4) = 28 m/s So, length of the train = 28 × 10 = 280 metres Relative speed of the bike with respect to the train = 33 – 28 = 5 m/s So, time taken by the bike to cross the train = (280/5) = 56 seconds