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math

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john and tom race around a circular track,divided like the face of a clock,into 12 sections.if john gives tom 4 sections start in advance and runs half as fast as tom.at what point on the track will he overtake tom

  • math -

    When they meet,
    let the number of laps covered by John (the slower) be n
    So number of sections covered by John = 12n
    In that same time, Tom has covered 12n-4 sections
    Time = distance/rate
    Tom's time = 12n/2
    John's time = (12n-4)/1
    12n/2 = 12n-4
    6n = 12n-4
    6n=4
    n= 2/3

    He will catch him at the 8 section mark of the first lap


    Tom's time = 12n/2 = 6n = 6(2/3) = 4 units of time
    John's time = (12n-4)/1 = 12(2/3)-4 = 4 units of time ----- ✔
    Tom's rate = Tom's distance/4 = 8/4 = 2 units of distance/units of time
    John's rate = 4/4 = 1 unit of distance/time ---- ✔

  • math -

    this is a little bit hard,still not understand

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