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Math Help - 2 walkers different strides

  1. #1
    MonsterTrainer
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    2 walkers different strides

    Math

    Jodi and Jim take a walk in the park. They both start out on their left foot. Jodi's step is only 2/3 of Jim's. At which step for Jodi and which step for Jim will they be ready to take a "left foot step" together again?
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  2. #2
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    Try this way of looking at the problem. Draw a sequence of lines each 2/3 inch long starting on the margin of your notepad and alternately labelling them left, right. Draw another sequence of lines just below that, starting at the same margin, each 1 inch long and alternately labelling them left, right. You should see that each LR pair in 4/3 inch long on one row and 2 inches long on the other. You want to know when they next align: in other words, when a mutiple of 4/3 is next equal to a multiple of 2. You'll find that 3 x (4/3) = 2 x (2) so the two are next in step after three double (LR) steps of one and two of the other.
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  3. #3
    MHF Contributor
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    a)It could be that Jodi's and Jim's steps are synchronized--that is, they step on their left and right feet at exactly the same time. It is only that Jodi's steps are 2/3 as long as Jim's.

    -----------------
    b)This maybe is what you mean.

    b.1) When Jim's left foot touches the ground again, Jodi's left foot is still on air, and still 1/3 short of the way to the ground.
    And then, after the 2nd touching on the ground of Jim's left foot, the left foot of Jodi is (1/3 +1/3) = 2/3 of the way.
    And then, on the 3rd touching on the ground of Jim's left foot, the left foot of Jodi is (2/3 +1/3) = 1 of the way, or it still on the ground.

    Count those steps.
    Jim's left foot makes 3 touchings on the ground.
    Jodi's left foot makes 2 touchings.
    Jim's and Jodi's left feet are again on the ground at the same time.

    Another one:
    b.2)
    Let
    m = number of times the left foot of Jim touches the ground.
    d = number of times the left foot of Jodi touches the ground.

    d = (2/3)m

    When m = 1, d = (2/3)(1) = 2/3
    when m = 2, d = (2/3)(2) = 4/3
    when m = 3, d = (2/3)(3) = 6/3 = 2 ---------answer.

    ---------
    Edited.

    If by step you mean "left-right" = one step; "right-left" = another step; or, "left-right-left" is two steps, then double the numbers found above because the numbers above count left-right-left as one step only.
    Thus,
    6 steps for Jim while 4 steps by Jodi and their left feet are both on the ground, at the same time, again. -------answer.
    Last edited by ticbol; August 19th 2005 at 02:23 AM.
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