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Solution


Q.

A train covered a certain distance at a uniform speed. If the train would have been 6 km/h faster, it would have taken 4 hours less than the scheduled time. And, if the train were slower by 6 km/hr; it would have taken 6 hours more than the scheduled time. Find the length of the journey.

Ans.

(720)

Let the actual speed of the train be x km/hr and let the actual time taken be y hours.

Distance covered is xy km If the speed is increased by 6 km/hr, then time of journey is reduced by 4 hours i.e., when speed is (x+6)km/hr, time of journey is (y−4) hours.

∴ Distance covered = (x + 6)(y − 4)

⇒ xy = (x + 6)(y − 4) ⇒ −4x + 6y − 24 = 0 ⇒ −2x + 3y −12 = 0               ………….(i)

Similarly xy = (x − 6)(y + 6) ⇒ 6x − 6y − 36 = 0 ⇒ x − y − 6 = 0              …………(ii)

Solving (i) and (ii) we get x = 30 and y = 24

Putting the values of x and y in equation (i), we obtain

Distance = (30 × 24)km = 720km.

Hence, the length of the journey is 720km.