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Question

# An express train takes 1hour less than a passenger train to travel 132 Km between Mysore and Bangalore (without taking into consideration the time they stop at intermediate stations). If the average speed of Express train is 1 Km/h more than that of the passenger train, find the average speeds of the train.

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Solution

## ● A correction in your question. Average speed of express train is 11km/hr more than passenger train. ○ Solution:- Let, average speed of the passenger train be 'x' km/hr the average speed of the express train be (x + 11) km/hr Distance between Mysore and Bangalore = 132 km It is given that the time taken by the express train to cover the distance of 132 km is 1 hour less than the passenger train to cover the same distance. So, time taken by passenger train = 132/x hr The time taken by the express train = {(132)/x+11} hr Now, according to the question {132/(x+11)} = 132/x + 1 [ After taking L.C.M. of 132/x +1 and then solving it we get (132+x)/x. ] {132/(x+11)} = (132+x)/x By cross multiplying, we get, 132x = x²+132x+11x+1452 x² + 11x - 1452 = 0 x² + 44x - 33x - 1452 = 0 x(x+44) - 33(x+44) = 0 (x+33) (x+44) = 0 x - 44 or x = 33 As the speed cannot be in negative therefore, x = 33 ◎ the speed of the passenger train = 33km/hr ◎ speed of express train is 33 + 11 = 44 km/hr

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