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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
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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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0x(x8)/(x+x8) = 3 solve for x

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2the working rate of Jimmy is W/x, where W is the work to be done. The working rate of Harry is W(x8) whereas the working rate when both Jimmy and Harry work together is: \[\frac{W}{x} + \frac{W}{{x  8}}\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2so, 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

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2oops..the working rate of Harry is W/x8

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so we now find a common denominator?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2the common denominator, is: 3x(x8)

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2and we got this equivalent equation: \[\Large 3\left( {x  8} \right) + 3x = x\left( {x  8} \right)\] with the condition: x8>0 since x8 is a time which has to be positive

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2I simplify that equation, nd I get this: \[\Large \begin{gathered} 3x  24 + 3x = {x^2}  8x \hfill \\ {x^2}  14x + 24 = 0 \hfill \\ \end{gathered} \]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2the 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

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2oops..only x=12 is acceptable

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so the first equation works?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Thanks:) So Jimmy can work 12 hours alone?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2yes! Jimmy works for x=12 hours only
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