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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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

Mathematics
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x(x-8)/(x+x-8) = 3 solve for x
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: \[\frac{W}{x} + \frac{W}{{x - 8}}\]

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Other answers:

I understand:)
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
oops..the working rate of Harry is W/x-8
So now do we do?
so we now find a common denominator?
the common denominator, is: 3x(x-8)
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
ok, ok:)
I simplify that equation, nd I get this: \[\Large \begin{gathered} 3x - 24 + 3x = {x^2} - 8x \hfill \\ {x^2} - 14x + 24 = 0 \hfill \\ \end{gathered} \]
uh huh! :)
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
oops..only x=12 is acceptable
so the first equation works?
Thanks:) So Jimmy can work 12 hours alone?
yes!
yes! Jimmy works for x=12 hours only
Thanks!
:)

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