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Math Help - Problem Solving

  1. #1
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    Problem Solving

    If 8 workers can plough a 6 ha field in 5 hours, how long will it take to plough a 9 ha field with 5 workers working at the same rate?

    I can never get these questions. Can someone please help me?
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  2. #2
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    Quote Originally Posted by xwrathbringerx View Post
    If 8 workers can plough a 6 ha field in 5 hours, how long will it take to plough a 9 ha field with 5 workers working at the same rate?

    I can never get these questions. Can someone please help me?
    "8 workers can plough a 6 ha field in 5 hours" therefore (8)(5) = 40 man-hours are required to plough a 6 ha field therefore 40/6 man-hours are required to plough a 1 ha field.

    Therefore a 9 ha field requires 9 (40/6) = 60 man-hours. 60 man-hours divided by 5 workers = 12 hours.

    So it takes 12 hours for 5 workers to plough a 9 ha field.

    If you want to be PC you can replace man-hours with person-hours.
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  3. #3
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    Another way is to simply figure out that there is an direct and inverse proportionality.
    Let t, f, and w denote time, ha field, and workers, respectively. Obviously, more workers mean less time and more field means more time. Therefore:

    t = \frac{kf}{w}

    Where k is a constant. If you plug in your given, you get k to be:
    k = \frac{40}{6}

    \implies t = \frac{40f}{6w}

    Plugging in f = 9 and w = 5, we get t = 12.
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