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At the beginning at a walk, Alex and Beth are 2.2 miles apart. If they leave at the same time and walk in the same direction, Alex overtakes Beth in 11 hours. If they walk towards each other, they meet in 1 hour. What are there speeds?

Alex? mph
Beth? mph

  • math -

    2.2/(a+b) = 1
    2.2/(a-b) = 11

    That is, the time to cover 2.2 miles with their combined speeds is 1 hur

    Alex overtakes Beth at a speed of a-b, and takes 11 hours to cover the extra 2.2 miles.

    rearrange things a bit to get

    a + b = 2.2
    11a - 11b = 2.2

    or,

    11a + 11b = 24.2
    11a - 11b = 2.2
    22b = 22
    b = 1
    a = 1.2

    Beth walks at 1 mph
    Alex walks at 1.2 mph

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