SOLUTION: working together, jamie and Juan can complete a job in 6 hours. It would take Jamie 9 hours longer than Juan to do the job alone. How long would it take Juan alone?

Question 233334: working together, jamie and Juan can complete a job in 6 hours. It would take Jamie 9 hours longer than Juan to do the job alone. How long would it take Juan alone?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
working together, jamie and Juan can complete a job in 6 hours. It would take Jamie 9 hours longer than Juan to do the job alone. How long would it take Juan alone?
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together rate = 1/6 job/hr
Jamie rate = 1/(x+9) job/hr
Juan rate = 1/x job/hr
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Equation:
rate + rate = together rate
1/x + 1/(x+9) = 1/6
(x+9+x)/(x(x+9)) = 1/6
(2x+9)/[x^2+9x] = 1/6
Cross-multiply and solve for "x":
12x + 54 = x^2+9x
x^2 - 3x - 54 = 0
x^2 - 9x + 6x - 54 = 0
x(x-9) + 6(x-9) = 0
(x-9)(x+6) = 0
Positive solution:
x = 9 hrs (amount of time it would take Juan to do the job)
x+9 = 18 hrs (amt. of time for Jamie to do the job)
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Cheers,
Stan H.
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