Question

A train covered a certain distance at a uniform speed. If the train would have 10km/h faster, it would have taken 2 hours less than the scheduled time. And if the train were slower 10km/h; it would have taken 3 hours more than the scheduled time. Find the distance covered by the train.

Answer 1

Let the speed of the train by x km/hr

And the time taken by the train be ‘y’ hrs

Distance traveled by the train is x.y = xy

Case I

If the train would have been 10 km/hr faster, it would have taken 2 hours less than the scheduled time.

⇒ (x + 10) (y - 2) = xy

⇒ -2x + 10y = 20

⇒ x – 5y = -10 ---------------- (1)

Case II

If the train were slower by 10 km/hr, it would have taken 3 hours more than the scheduled time

⇒ (x - 10) (y +  3) = xy

⇒ 3x – 10y - 30 = 0

⇒ 3x – 10y = 30 ----------------(2)

Solving the equations (1) and (2), we get y = 12, x = 50

Therefore, the distance of the journey = 50 × 12 = 600 km.