document.write( "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? \n" ); document.write( "

Algebra.Com's Answer #829496 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "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

\n" ); document.write( " $\"%28240x%2B20%29%5E2%2B%28200x%29%5E2=250%5E2\"$

\n" ); document.write( "Solving that equation algebraically is a bit messy, but not too awful; using a graphing calculator would be a lot easier.

\n" ); document.write( "But since the numbers in the problem are whole numbers, we can guess the solution by thinking about Pythagorean Triples.

\n" ); document.write( "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).

\n" ); document.write( "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.

\n" ); document.write( "ANSWER: 5 minutes plus another 45 minutes after noon -- at 12:50pm.

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