Question

A train travels 360 km at a uniform speed. If the speed had been 5 km/hr more, it would have taken 1 hour less for the same journey. Form a quadratic equation to find the speed of the train.

Answer 1

Consider the given question,

Distance $=360$ km

Speed $=x$ km/hr

When speed is increase $(x+5)$ km/hr

Given expression is written as,

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

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

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

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

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

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

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

$\Rightarrow x=40,-45$

But, speed can not be negative.

Hence, speed is $40$ km/hr