Question

A train travels 360 km at a uniform speed .if the speed had been 5 km/h more it would have taken 1hour less for the same journey

Answer 1

Let the speed of the train be x.

The new speed is x + 5

The time taken before the speed is increased is :

360/x

The time taken after the speed is increased is

360/(x + 5)

This time is 1 hr less.

We equate these two as follows :

360/x = 360/(x + 5) + 1

360(x + 5) = 360x + x (x + 5)

360x + 1800 = 360x + x² + 5x

x² + 5x - 1800 = 0

x² + 45x - 40x - 1800 = 0

x ( x + 45) - 40(x + 45) = 0

(x + 45) (x - 40) = 0

x = - 45 or 40

We take the speed which is positive.

The speed of the train is thus 40km/h