Question

Question 8
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

Let the speed of the train be x km/hr.
Time taken to cover 360 km $=\frac{360}{x}$ hr.
According to the question,
$\Rightarrow (x+5)(\frac{360}{x}-1)=360$
$\Rightarrow 360-x+\frac{1800}{x}-5=360$
$\Rightarrow x^2+5x-1800=0$
$\Rightarrow x^2+45x-40x-1800=0$
$\Rightarrow x(x+45)-40(x+45)=0$
$\Rightarrow (x+45)(x-40)=0$
$\Rightarrow x=40,-45$
However, speed cannot be negative.
Therefore, the speed of train is 40 km/h.