Question

A train travels 180 km at a uniform speed. If the speed had been 9 km/hr more, it would have taken 1 hour less for the same journey. Find the speed of the train.

Answer 1

Let the speed of train be x km/h.

Distance = 180 km

So, time = $\frac{180}{x}$

When speed is 9 km/h more, time taken = $\frac{180}{x+9}$

According to the given information, $\frac{180}{x}-\frac{180}{x+9}=1$

$\Rightarrow 180(x+9)-180x=x(x+9)\Rightarrow x^2+9x-1620=0\Rightarrow x^2+45x-36x-1620=0$

$\Rightarrow x(x+45)-36(x+45)=0\Rightarrow x=-45,36$

Discarding the negative value, speed of the train = 36 kmph.