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An airplane flew in a direct line from its base at the rate of 300miles an hour and returned over the same route at the rate of 250miles an hour, requiring 15min longer of the returned trip . How far from its base did it fly

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Since d = rt.

We know that d = 300t and d = 250(t+15).

Setting these equal gives 300t = 250(t+15).

Multiplying this out gives 300t  = 250t + 3750.

Subtract off 250t from both sides and get 50t = 3750.

Divide both sides by 50 and get t = 75 (yes, that's 3 days and 3 hours).

Put that back in the equation d = 300t and get d = 300*75 = 22,500.
That is, d = 22,500 miles.

Checking this gives 22,500 = 300 * 75, and that is true.
It also gives 22,500 = 250(75+15) = 250*90, and that is also true.

Occasionally math problems don't apply to reality.  See, as a side note, since there are only roughly 25,000 miles around the earth, it might have been quicker to fly 1,500 miles in the opposite direction.  At 300 mph this would have only taken 5 hours and at 250 mph this would have taken 6 hours ...  


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Scott A Wilson


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