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Math Help - jockey puzzle

  1. #1
    Newbie
    Joined
    Oct 2008
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    1

    jockey puzzle

    Can anybody help with this problem?

    lightning lady and stirling monarch set off from the same point on their circular training track, with their jockeys riding them in opposite directions. the first time they meet, lightning lady has run 500m. the next time they meet stirling monarch still has 200m to go before he finishes his first lap. how far is it around their track?
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  2. #2
    MHF Contributor
    Joined
    Apr 2005
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    Let d = distance around their track.
    Let L = speed of ligtning lady
    Let S = speed of stirling monarch

    When Ligthning Lady (LL) traveled 500m, SM traveled (d-500) m, and that is for the same time t1.
    So,
    t1 = 500/L = (d -500)/S
    L = 500S /(d-500)

    When LL continued and traveled [(d-500) +200]m, SM traveled (500 -200)m, and that is also in the same t2.
    So,
    t2 = [(d-500) +200] /L = (500-200) /S
    (d-300)/L = 300/S
    L = (d-300)S /300

    L = L
    500S /(d-500) = (d-300)S /300
    Cross multiply,
    500(300) = (d-500)(d-300)
    150,000 = d^2 -1600d +150,000
    0 = d^2 -1600d
    0 = d -1600
    d = 1600 meters ---------answer.
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