Question

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

Answer 1

Given distance$=360$ km.

Let the speed of the train be $x$ km/hr.

Speed when increased by $5$ km/hr $=(x+5)$ km/hr

$\frac{360}{x}-\frac{360}{(x+5)}=1$

$\frac{[360x+1800-360x]}{x(x+5)}=1$

$x^2+5x-1800=0$

$x^2+45x-40x-1800=0$

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

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

$x=40,-45$

The speed of the train is $40$ km/hr.