#### 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 the quadratic eqiation to find the speed of the train.

#### Solution

Let Speed of train be x km/hr

Distance travelled by train = 360 km

We know that

`"Time of total"="Distance travelled"/"Speed of the train"=360/x hr`

If speed had been 5 km/hr more ⇒ (x + 5)km/hr

`"Time of travel"="Distance travelled"/"Speed of the train"=360/(x+5) hr`

Give that,

Time of travel when speed is increased is 1 hour less than of the actual time of travel

`rArr360/x-360/(x+5)=1`

`rArr360(1/x-1/(x+5))=1`

`rArr360((x+5-x)/(x(x+5)))=1`

⇒ 360(5) = x(x + 5)

⇒ x^{2} + 5x = 1800

⇒ x^{2} + 5x + 1800 = 0

∴ The required quadratic equation to find the speed of the train is x^{2} + 5x + 1800 = 0