Question

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

Answer 1

Let the speed of the train be $xkmph$

The time taken by the train to travel $180km$ is $\frac{180}{x}h$

The increased speed is $x+9$

The time taken is $\frac{180}{x+9}$

According to the question,

The time taken is $\frac{180}{x}-1$

$⟹\frac{180}{x}-1=\frac{180}{x+9}$

$⟹\frac{180-x}{x}=\frac{180}{x+9}$

$⟹180x-x^2+1680-9x=180x$

$⟹x^2+9x-1680=0$

$⟹x^2+45x-36x-1680=0$

$⟹x(x+45)-36(x+45)=0$

$x=36,-45$

Speed cannot be negative (In this case,)

So The speed of the train is $36kmph$