Question

A passenger train takes 5 hours less for a journey of 252 km if its speed is increased by 35 kmph from its normal speed.the normal speed in kmph (to the nearest integer ) is

Answer 1

The normal speed of the train is 28 kmph.

Explanation

Lets assume, the normal speed of the train is  $x$ kmph.

Total distance of the journey is 252 km.

As, $Time=\frac{Distance}{Speed}$

So, the time required in normal speed $=\frac{252}{x}$ hours.

and if the speed is increased by 35 kmph, then the time required $=\frac{252}{x+35}$ hours.

Given that, the time required in increased speed is 5 hours less than the time in normal speed. That means....

$\frac{252}{x}-\frac{252}{x+35}=5\\ \\ \frac{252x+8820-252x}{x(x+35)}=5\\ \\ \frac{8820}{x(x+35)}=5\\ \\ 5x(x+35)=8820\\ \\ x(x+35)=1764\\ \\ x^2+35x-1764=0\\ \\ (x-28)(x+63)=0$

Using zero-product property.....

$x-28=0\\ x=28\\ \\ and\\ \\ x+63=0\\ x=-63$

(Negative value is ignored as the speed can't be negative)

So, the normal speed of the train is 28 kmph.