Question

A train travels a distance of $480km$ at a uniform speed. If the speed had been $8km/h$ less, then it would have taken $3$ hours more to cover the same distance. We need to find the speed of the train

Answer 1

Let the speed of the train $=x$km/hr

Distance $=480$km

Time taken by the train to cover the distance of $480$km$=\frac{480}{x}$hrs

Now, according to the given condition,

$\frac{480}{x-8}-\frac{480}{x}=3$

$\Rightarrow 480(\frac{1}{x-8}-\frac{1}{x})=3$

$\Rightarrow \frac{x-8+8}{x(x-8)}=\frac{3}{480}$

$\Rightarrow x^2-8x=1280$

$\Rightarrow x^2-8x-1280=0$

$\Rightarrow x^2-40x+32x-1280=0$

$\Rightarrow x(x-40)+32(x-40)=0$

$\Rightarrow x-40=0$ or $x+32=0$

$\Rightarrow x=40$ or $x=-32$

But the speed of the train cannot be negative.Hence, the speed of the train is $40$km/hr