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Math Help - distance and rate problem

  1. #1
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    distance and rate problem

    how long will it take someone running at 12 mph to catch up to someone walking at 5 mph with an hour and half head start?

    I keep getting 15/24 but the answer sheet says it is 15/14? is the answer on the answer sheet a typo or am i doing it wrong?
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  2. #2
    Senior Member eumyang's Avatar
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    I'm assuming here that t = time for the jogger:
    walker: d = 5(t + 1.5)
    jogger: d = 12t

    Set the equations equal:
    \begin{aligned}<br />
5(t + 1.5) &= 12t \\<br />
5t + 7.5 &= 12t \\<br />
7t &= 7.5 \\<br />
t &= \frac{7.5}{7} \\<br />
t &= \frac{15}{14}<br />
\end{aligned}
    15/14 hours ≈ 1 hr, 4 min, 17.14 sec
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  3. #3
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    Maa'le edomim-near Jerusalem
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    look at this !

    look at this sketch!
    Attached Thumbnails Attached Thumbnails distance and rate problem-1.jpg  
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  4. #4
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    ooohh! i get it! thanks a lot!
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