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.

Answer 1

Let the 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 the 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`

⇒ `(300 xx 5)/(x(x + 5)) = 2`

⇒ `1500/(x^2 + 5x) = 2`

⇒ 1500 = 2x² + 10x

⇒ x² + 5x − 750 = 0

⇒ x² + 30x − 25x − 750 = 0

⇒ (x + 30) (x − 25) = 0

⇒ x = 25, −30

Since speed cannot  be negative, the original speed of the train is 25 km/hour.