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.

Answer 1

We have,

Total distance $=360km.$

Let the speed $=xkm/hr.$

Increase speed $=(x+5)km./hr.$

Then,

We know that,

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

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

$\Rightarrow \frac{360x+1800-360x}{x^2+5x}=1$

$\Rightarrow 1800=x^2+5x$

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

$\Rightarrow x^2+(45-40)x-1800=0$

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

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

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

If

$x+45=0$

$x=-45$

If

$x-40=0$

$x=40$

The speed is

$x+5$

$40+5$

$=45km/hr.$

Hence, this is the answer.