Question

An express train takes 1 hour 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 the express train is 11 km/hr more than that of the passenger train, find the average speed of the two trains.

Answer 1

Let the average speed of the passenger train be 'x' km/hr and 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

After taking L.C.M. of 132/x + 1 and then solving it we get (132 + x)/x .

Now,

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 or the speed of the passenger train = 33 km/hr and the speed of express train is 33 + 11 = 44 km/hr.