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Tuesday, April 20, 2010

Fun Math Problem

Arlene is a serious runner. Every morning she runs one loop of her route. She runs downhill at 6 mph. She runs uphill at 2 mph. If Amy runs her route clockwise, it takes her 1 hour to complete 1 loop. If she runs the route counter-clockwise, it takes her 2 hours to complete 1 loop. Find the distance of 1 loop.


  1. Are we assuming that half of the route is downhill and half is uphill?

  2. You can assume that. Or choose 3/4 & 1/4

  3. I got 4.5 miles. But I must say as a runner that the problem makes no sense. Times are a function of vertical gain as well as horizontal distance. But in a loop these two numbers are equal, so there can't be such a huge difference in times!

    Pretty cool problem, though!

    P.S. I love the "Lab Mice Puzzles", Tom!!

  4. Your solution is correct George! Thanks for the positive feedback about the Lab Mice Puzzles. Visit: to order 2 books of them! Spread the word!