Question
Speed of a car is (v + 5) km/h, which is 7 km/h less
than that of bike. Time taken by car to cover 72 km is 25% less than the time taken by bike to cover 120 km. Length of a train is (5v + 11) metres. If speed of train is (v - 2) m/s, then find the time taken (in seconds) by train to cross a man standing on a platform of length 360 metres.Solution
Speed of bike = v + 5 + 7 = (v + 12) km/h 72 ÷ (v + 5) = (3/4) × 120 ÷ (v + 12) Or, 72(v + 12) = 90(v + 5) Or, 72v + 864 = 90v + 450 Or, 18v = 414 Or, v = 23 Length of train = 5 × 23 + 11 = 126 metres Speed of train = 23 − 2 = 21 m/s Since we need to calculate the time taken by train to cross the man standing on the platform, so the length of the platform will not be considered. Required time = 126 ÷ 21 = 6 seconds
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