Question

A train travels 180 km at a uniform speed. If the speed had been 9 km/hr more, it would have taken 1 hour less for the same journey. Find the speed of the train.

Answer 1

Let the original speed of the train = x km/hr.

Time taken for 180 km = `180/x` hours

Increased speed = (x + 9) km/hr.

New time taken = `180/(x + 9)` hours.

`180/x - 180/(x + 9) = 1`

`(180(x + 9) - 180x)/(x(x + 9)) = 1`

1620 = x² + 9x

x² + 9x – 1620 = 0

Solve for x

(x – 36) (x + 45) = 0

x = 36 or x = –45

Since speed cannot be negative, the speed of the train is 36 km/hr.