one hour out of the station, a train engine develops trouble that slows the trai

Question

one hour out of the station, a train engine develops trouble that slows the train to 3/5 of its average speed up to the time of the failure. Continuing at this reduced speed, it reaches its destination two hours late. Had the trouble occured 50 miles beyond, the delay would have been reduced by 40 minutes. Find the distance from the station to the destination.

Explanation / Answer

Let the distance be X and the average velocity be V In the first hour it travels V*1 miles the time taken after that = (X-V)/0.6*V then the time taken in the first case= (X/V) +2 = 1+ (5/3)( X-V)/V => 2/3(X/ V) = 1+5/3 => X= 4V second case: (X/V)+ (2-2/3) = (V+50)/V + (X-(V+50))/(3/5)V 4+ (4/3) = 1+ (50/V) + 5/3 (4) - 5/3 -(5/3) * (50/V) => 2/3 (50/V) = 6-4-4/3=2/3 => V= 50 mph distance : X=4*50=200 miles

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