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.
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Solution:
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.
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