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. Find the speed of the train.

• A. 25 km/h
• B. 30 km/h
• C. 35 km/h
• D. 40 km/h

Answer 1

The correct option is D

40 km/h

Let the speed of the train be x km/hr.
Time taken to cover 360 km $=\frac{360}{x}$ hr.
According to the question,

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

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

360 ($\frac{5}{x^2+5x})=1$

$1800=x^2+5x$
$\Rightarrow x^2+5x-1800=0$
$\Rightarrow x^2+45x-40x-1800=0$
$\Rightarrow x(x+45)-40(x+45)=0$
$\Rightarrow (x+45)(x-40)=0$
$\Rightarrow x=40,-45$
However, speed cannot be negative.
Therefore, the speed of train is 40 km/h.