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 the quadratic equation to find the speed of the train.

Given:

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.

To do:

Here, we have to form the quadratic equation to find the speed of the train.

Solution:

Let the speed of the train be $x$ km/hr.

Time taken to travel $360$ km $=\frac{360}{x}$ hours

Time taken to travel $360$ km when the speed had been $5$ km/hr more $=\frac{360}{x+5}$ hours

Therefore,

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

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

$360x+1800-360x=x^2+5x$

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

The required equation is $x^2+5x-1800=0$.