Mileage - Futility Closet

Mileage

I leave my front door, run on a level road for some distance, then run to the top of a hill and return home by the same route. I run 8 mph on level ground, 6 mph uphill, and 12 mph downhill. If my total trip took 2 hours, how far did I run?

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The length of the hill is immaterial — if I average 6 mph climbing and 12 mph descending, then my average speed on the hill is 8 mph, just as on level ground. So in 2 hours I ran 16 miles. (A few people have asked why my average speed on the hill isn’t (6 + 12) / 2 = 9 mph. Remember that I’ll spend more time climbing than descending — for example, if the hill segment is 4 miles long, then I’ll spend 4/6 hours up + 4/12 hours down = 1 hour covering 8 miles.)

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April 2, 2015April 12, 2015 | Puzzles