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  Number and Math Play

Uphill, Downhill
 
Q Grandma walked up a hill at the rate of 2 miles an hour, turned around as soon as she got to the top, and walked down the hill at the rate of 4 miles an hour. The whole trip took her 6 hours. How many miles is it to the top of the hill?


 
A

Here's one of several ways to figure out the answer: Grandma walked 1 mile up the hill in 30 minutes and 1 mile down in 15 minutes. In other words, 1 mile took her 45 minutes round trip. The whole trip took her 6 hours, or 360 minutes; if you divide the overall time (360 minutes) by the time it took to do 1 mile (45 minutes), you find out that the overall length of the hill is 8 miles.

STRATEGY: Make it simpler.

Source: Inspired by a puzzle in The Adler Book of Puzzles and Riddles, or Sam Loyd Up-to-Date, Irving and Peggy Adler. New York: John Day, 1962.