Question

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

Answer 1

Let the usual speed of train be x km/hr then

Increased speed of the train = (x + 5)km/hr

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

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

Therefore,

`150/x-150/(x+5)=1`

`(150(x+5)-150x)/(x(x+5))=1`

`(150x+750-150)/(x^2+5x)=1`

`750/(x^2+5x)=1`

750 = x² + 5x

x² + 5x - 750 = 0

x² - 25x + 30x - 750 = 0

x(x - 25) + 30(x - 25) = 0

(x - 25)(x + 30) = 0

So, either

x - 25 = 0

x = 25

Or

x + 30 = 0

x = -30

But, the speed of the train can never be negative.

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