Question
Train P takes 24 seconds to pass
a tree and 34 seconds to pass through a 150-meter-long tunnel. Train Q, which is 440 meters long, takes 17.6 seconds to pass a tree. If trains P and Q are traveling toward each other, how much time will they take to completely cross each other?Solution
ATQ, Let the length of train ‘P’ = ‘d’ metres Then, distance covered by train ‘P’ in 24 seconds = ‘d’ metres Distance covered by train ‘P’ in 34 seconds = (d + 150) metres So, distance covered by train ‘P’ in (34 – 24) seconds = (d+ 150 – d) metres So, speed of train ‘P’ = 150 ÷ 10 = 15 m/s Length of train ‘P’ = 15 × 24 = 360 metres Speed of train ‘Q’ = 440 ÷ 17.6 = 25 m/s So, relative speed of train ‘P’ with respect to train ‘Q’ = 15 + 25 = 40 m/s Therefore, time taken by the trains to cross each other = (360 + 440) ÷ 40 = 20 seconds
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