Question
The ratio of the speed of a train to a bike is 5:2 and the bike travels 60 km less than the train in the same time duration. If the time taken by the train to travel its distance is 4 hours, then find the speed of the bike.
Solution
ATQ, Distance = speed × time Time = distance/speed Let the distance travelled by the train = d km Let the speeds of the train and bike be 5x km/hr and 2x km/hr, respectively. Since both travel for the same time, d / (5x) = (d − 60) / (2x) Cross-multiplying, 2d = 5d − 300 2d − 5d = −300 −3d = −300 d = 100 km Now, time taken by the train = 4 hours, so d / (5x) = 4 100 / (5x) = 4 100 = 20x x = 5 The speed of the bike = 2 × 5 = 10 km/hr
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