#### Question

A train covers a distance of 300 km at a uniform speed. If the speed of the train is increased by 5 km/hour, it takes 2 hours less in the journey. Find the original speed of the train

#### Solution

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

Thus, time taken to travel 300 km = `300/x` hours.

Now when the speed is increased then time is reduced by 2 hours.

Time taken to cover 300 km with speed x km/hr − Time taken to cover 300 km with increased speed = 2 hours

`300/x - 300/(x + 5) = 2`

`=> (300[x + 5 - x])/(x(x + 5)) = 2`

`=> (300xx 5)/(x(x+5)) = 2`

`=> 1500/(x^2 + 5x) = 2`

`=> 1500 = 2x^2 + 10x`

`=> x^2 + 5x - 750 = 0`

`=> x^2 + 30x - 25x - 750 = 0`

`=> (x + 30) (x - 25) = 0`

=> x = 25, -30

Since speed cannot be negative so the original speedof the trian = 25 km/hour