Question

 A passenger train takes one hour less for a journey of 150 km if its speed is increased 5 km/hr from its usual speed. Find the usual speed of the train.

Answer 1

Let’s assume the usual speed of train as x km/hr

Then, the increased speed of the train = (x + 5) km/hr

Using, speed = distance/ time

Time taken by the train under usual speed to cover 150 km = 150/x hr

Time taken by the train under increased speed to cover 150 km = 150(x + 5)hr

Given, that the difference in the times is 1 hour.

This can be expressed as below:

750 = x² + 5x

x² + 5x – 750 = 0

x² – 25x + 30x -750 = 0 [by factorisation method]

x(x – 25) + 30(x – 25) = 0

(x – 25) (x + 30) = 0

x = 25  or x = -30 (neglected as the speed of the train can never be negative)

Hence, the usual speed of the train is x = 25 km/hr