Question
A train of length (Q + 30) metres passes a pole in 18
seconds and a tunnel of length 540 metres in 36 seconds. Find the time (in seconds) the train will take to cross a bridge of length '2Q' metres.Solution
ATQ,
Speed of train = [(Q + 30) ÷ 18] m/s
Also, speed = [(Q + 30 + 540) ÷ 36]
So, [(Q + 30) ÷ 18] = [(Q + 570) ÷ 36]
Or, [(Q + 30) ÷ 1] = [(Q + 570) ÷ 2]
Or, 2 × (Q + 30) = Q + 570
Or, 2Q + 60 = Q + 570
Or, Q = 510
Speed = [(510 + 30) ÷ 18] = 540 ÷ 18 = 30 m/s
Length of train = Q + 30 = 540 metres
Required time = (540 + 2 × 510) ÷ 30 = 1560 ÷ 30 = 52 seconds
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