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anonymous

  • one year ago

Harry can rake the leaves in the yard 8 hours faster than his little brother Jimmy can. If they work together, they can complete the job in 3 hours. Using complete sentences, explain each step in figuring out how to determine the time it would take Jimmy to complete this job on his own

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  1. anonymous
    • one year ago
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    @Michele_Laino

  2. anonymous
    • one year ago
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    x(x-8)/(x+x-8) = 3 solve for x

  3. Michele_Laino
    • one year ago
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    the working rate of Jimmy is W/x, where W is the work to be done. The working rate of Harry is W(x-8) whereas the working rate when both Jimmy and Harry work together is: \[\frac{W}{x} + \frac{W}{{x - 8}}\]

  4. anonymous
    • one year ago
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    I understand:)

  5. Michele_Laino
    • one year ago
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    so, using your data we can write: \[\Large \frac{W}{x} + \frac{W}{{x - 8}} = \frac{W}{3}\] or after a simplification: \[\Large \frac{1}{x} + \frac{1}{{x - 8}} = \frac{1}{3}\] please solve that last equation for x

  6. Michele_Laino
    • one year ago
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    oops..the working rate of Harry is W/x-8

  7. anonymous
    • one year ago
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    So now do we do?

  8. anonymous
    • one year ago
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    so we now find a common denominator?

  9. Michele_Laino
    • one year ago
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    the common denominator, is: 3x(x-8)

  10. Michele_Laino
    • one year ago
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    and we got this equivalent equation: \[\Large 3\left( {x - 8} \right) + 3x = x\left( {x - 8} \right)\] with the condition: x-8>0 since x-8 is a time which has to be positive

  11. anonymous
    • one year ago
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    ok, ok:)

  12. Michele_Laino
    • one year ago
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    I simplify that equation, nd I get this: \[\Large \begin{gathered} 3x - 24 + 3x = {x^2} - 8x \hfill \\ {x^2} - 14x + 24 = 0 \hfill \\ \end{gathered} \]

  13. anonymous
    • one year ago
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    uh huh! :)

  14. Michele_Laino
    • one year ago
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    the solution of that quadratic equation are: \[\Large \begin{gathered} x = \frac{{14 + \sqrt {{{\left( { - 14} \right)}^2} - 4 \times 1 \times 24} }}{{2 \times 1}} = 12 \hfill \\ \hfill \\ x = \frac{{14 - \sqrt {{{\left( { - 14} \right)}^2} - 4 \times 1 \times 24} }}{{2 \times 1}} = 2 \hfill \\ \end{gathered} \] please check my values. Only x012 is acceptable

  15. Michele_Laino
    • one year ago
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    oops..only x=12 is acceptable

  16. anonymous
    • one year ago
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    so the first equation works?

  17. anonymous
    • one year ago
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    Thanks:) So Jimmy can work 12 hours alone?

  18. Michele_Laino
    • one year ago
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    yes!

  19. Michele_Laino
    • one year ago
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    yes! Jimmy works for x=12 hours only

  20. anonymous
    • one year ago
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    Thanks!

  21. Michele_Laino
    • one year ago
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    :)

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