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Math Help - Lawnmower Problem

  1. #1
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    Lawnmower Problem

    The Smith family has two lawnmowers, one old and one new. Here is a table for how long it takes each son to mow the lawn using each lawnmower and working alone.

    New Old
    Johnny 2 hrs 2 hrs 30 min
    Jimmy 3 hrs 3 hrs 40 min

    How long does it take them working together:
    a. If Johnny uses the new one and Jimmy uses the old one?

    b. If Johnny uses the old one and Jimmy uses the new one?

    PLEASE HELP

    Thanks,

    Steve
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  2. #2
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    Quote Originally Posted by skweres1 View Post
    The Smith family has two lawnmowers, one old and one new. Here is a table for how long it takes each son to mow the lawn using each lawnmower and working alone.

    New Old
    Johnny 2 hrs 2 hrs 30 min
    Jimmy 3 hrs 3 hrs 40 min

    How long does it take them working together:
    a. If Johnny uses the new one and Jimmy uses the old one?

    b. If Johnny uses the old one and Jimmy uses the new one?

    PLEASE HELP

    Thanks,

    Steve
    Johnny's rates ... \frac{1 \, job}{2 \, hrs} and \frac{1 \, job}{(5/2) \, hrs} or \frac{2 \, jobs}{5 \, hrs}

    Jimmy's rates ... \frac{1 \, job}{3 \, hrs} and \frac{1 \, job}{(11/3) \, hrs} or \frac{3 \, jobs}{11 \, hrs}

    Jonny new , Jimmy old working together ...

    \left(\frac{1 \, job}{2 \, hrs} + \frac{3 \, jobs}{11 \, hrs}<br />
\right)(t \, hrs) = 1 \, job \, done<br />

    solve for t
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  3. #3
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    Hello, Steve!

    The Smith family has two lawnmowers, one old and one new.
    Here is a table for how long it takes each son to mow the lawn using each lawnmower and working alone.

    \begin{array}{c||c|c|}<br />
& \text{New} & \text{Old } \\ \hline \hline<br /> <br />
\text{Johnny} & \text{2 hrs} & \text{2 hrs, 30 min} \\ \hline<br />
\text{Jimmy} & \text{3 hrs} & \text{3 hrs, 40 min} \\ \hline<br />
\end{array}

    How long does it take them working together:

    (a) If Johnny uses the new one and Jimmy uses the old one?

    (b) If Johnny uses the old one and Jimmy uses the new one?

    (a) Using the new mower, Johnny takes mows the lawn in 2 hours
    . . In one hour, he mows \tfrac{1}{2} of the lawn.
    . . In x hours, he mows \frac{x}{2} of the lawn.

    Using the old mower, Jimmy takes 3\tfrac{2}{3} = \tfrac{11}{3} hours.
    . . In one hour, he mows \frac{1}{\frac{11}{3}} = \tfrac{3}{11} of the lawn.
    . . In x hours, he mows \frac{3x}{11} of the lawn.

    Working together, in x hours, they can mow: . \frac{x}{2} + \frac{3x}{11} \,=\,\frac{17x}{22} of the lawn.

    But in x hours, we expect to mow the entire lawn (1 lawn).


    There is our equation: . \frac{17x}{22} \:=\:1 \quad\Rightarrow\quad x \:=\:\frac{22}{17}


    Working together, they can mow the law in 1\tfrac{5}{17} hours.



    Use the same procedure for part (b).


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