Question
Speed of a car is (v + 3) km/h, which is 12 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 144 km. Length of a train is (5v + 14) metres. If speed of train is (v - 4) m/s, then find the time taken (in seconds) by train to cross a man standing on a platform of length 600 metres.Solution
Speed of bike = v + 3 + 12 = (v + 15) km/h 72 ÷ (v + 3) = (3/4) × 144 ÷ (v + 15) Or, 72(v + 15) = 108(v + 3) Or, 72v + 1080 = 108v + 324 Or, 36v = 756 Or, v = 21 Length of train = 5 × 21 + 14 = 119 metres Speed of train = 21 − 4 = 17 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 = 119 ÷ 17 = 7 seconds
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