SOLUTION: An airplane flying north at the rate of 240 miles per hour passed over a flying field at noon. A second plane flying east at 200 miles per hour passed the same field 5 minutes late

Question 1196589: An airplane flying north at the rate of 240 miles per hour passed over a flying field at noon. A second plane flying east at 200 miles per hour passed the same field 5 minutes later. When were they 250 miles apart?
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

The plane flying north at 240mph travels 20 miles in 5 minutes (1/12 of an hour). So the description of the problem leads to a right triangle with the "north" leg of length 20+240x miles and the "east" leg of length 200x miles, with the hypotenuse 250 miles. So algebraically we have

Solving that equation algebraically is a bit messy, but not too awful; using a graphing calculator would be a lot easier.

But since the numbers in the problem are whole numbers, we can guess the solution by thinking about Pythagorean Triples.

The hypotenuse is 250, so it would be nice if the two legs were either 70 and 240 (7-24-25 Pythagorean Triple) or 150 and 200 (15-20-25 Pythagorean Triple).

And some simple calculations show that the legs of 150 and 200 are obtained when x = 3/4, indicating the two planes are 250 miles apart 3/4 hour after the second plane passes the field.

ANSWER: 5 minutes plus another 45 minutes after noon -- at 12:50pm.

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