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

Let the train’s speed be x km/h and the time elapsed be y hours.

The entire distance is xy kilometers.

Scenario 1:

The speed improves by 10 kilometers per hour, while the time required decreases by 2 hours. The traveled distance remains xy kilometers.

(x+10)(y-2)=xy

Therefore, xy-2x+10y-20=xy

-2x+10y-20=0

-2x+10y=20…………………(1)

Scenario 2:

The time required rises by 3 hours when the speed lowers by 10 km/h.

However, the distance is still xy kilometers.

(x-10)(y+3)=xy

Therefore, xy+3x-10y-20=xy

3x-10y-30=0

3x-10y=30…………………(2)

x=50km/h

By this (2)

150-10y=30

y=12

So the distance is 50×12=600 km.