#### 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.

#### Solution

Let the original speed of train be x km/hr. Then,

Increased speed of the train = (x + 5)km/hr

Time taken by the train under usual speed to cover 360 km = `360/x`hr

Time taken by the train under increased speed to cover 360 km = `360/(x+5)`hr

Therefore,

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

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

`(360x+1800-360x)/(x^2+5x)=1`

`1800/(x^2+5x)=1`

1800 = x^{2} + 5x

x^{2} + 5x - 1800 = 0

x^{2} - 40x + 45x - 1800 = 0

x(x - 40) + 45(x - 40) = 0

(x - 40)(x + 45) = 0

So, either

x - 40 = 0

x = 40

Or

x + 45 = 0

x = -45

But, the speed of the train can never be negative.

Hence, the original speed of train is x = 40 km/hr