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Math Help - Work Problem

  1. #1
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    Smile Work Problem

    Dave can mow his lawn in 20 minutes less time than with a power mower that with his hand mower. One day, the power mower broke 15 minutes after he started mowing and he took 25 minutes more time to complete the job with the hand mower. How many minutes does Dave take to mow the lawn with the power mower?

    The book tells me to use this:

    rate of work x time worked = part of job completed

    Who can clarify this question for me?


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  2. #2
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    Quote Originally Posted by magentarita View Post
    Dave can mow his lawn in 20 minutes less time than with a power mower that with his hand mower. One day, the power mower broke 15 minutes after he started mowing and he took 25 minutes more time to complete the job with the hand mower. How many minutes does Dave take to mow the lawn with the power mower?

    The book tells me to use this:

    rate of work x time worked = part of job completed

    Who can clarify this question for me?

    1. Let t denote the time (measured in minutes) you need to mow the lawn by hand. Let L denote the area of the lawn.

    Then (t-20) is the time you need when you use a power mower.

    2. In one minute the hand mower has done \dfrac Lt of the lawn and
    in one minute the power mower has done \dfrac L{t-20} of the lawn. Therefore t > 20.

    3.
    \underbrace{\dfrac L{t-20} \cdot 15}_{work\ of\ power\ mower} + \underbrace{\dfrac Lt \cdot 25}_{work\ of\ hand\ mower} = L

    Divide through by L. Multiply by the denominators to get rid of the fractions:

    15t+25t-500 = t^2-20t~\implies~t^2-60t+500=0

    Solve for t.

    I've got t = 10 or t = 50. So the only possible solution is t = 50. (see #2.)
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  3. #3
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    ok

    Quote Originally Posted by earboth View Post
    1. Let t denote the time (measured in minutes) you need to mow the lawn by hand. Let L denote the area of the lawn.

    Then (t-20) is the time you need when you use a power mower.

    2. In one minute the hand mower has done \dfrac Lt of the lawn and
    in one minute the power mower has done \dfrac L{t-20} of the lawn. Therefore t > 20.

    3.
    \underbrace{\dfrac L{t-20} \cdot 15}_{work\ of\ power\ mower} + \underbrace{\dfrac Lt \cdot 25}_{work\ of\ hand\ mower} = L

    Divide through by L. Multiply by the denominators to get rid of the fractions:

    15t+25t-500 = t^2-20t~\implies~t^2-60t+500=0

    Solve for t.

    I've got t = 10 or t = 50. So the only possible solution is t = 50. (see #2.)
    The answer in the book is 30 minutes.

    How do I get 30 minutes?

    Thanks
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