SOLUTION: Working together, Rick and Juanita can complete a job in 6 hours. It would take Rick 9 hours longer than Juanita to do the job alone. How long would it take Juanita alone? Show you

Question 298661: Working together, Rick and Juanita can complete a job in 6 hours. It would take Rick 9 hours longer than Juanita to do the job alone. How long would it take Juanita alone? Show your work.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Working together, Rick and Juanita can complete a job in 6 hours. It would take Rick 9 hours longer than Juanita to do the job alone. How long would it take Juanita alone? Show your work.
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Together DATA:
time = 6 hrs/job ; rate = 1/6 job/hr
---
Juanita DATA:
time = x hrs/job ; rate = 1/x job/hr
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Rick = (x+9) hrs/job ; rate = 1/(x+9) job/hr
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Equation:
rate + rate = together rate:
1/x + 1/(x+9) = 1/6
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Multiply thru by 6x(x+9)
6(x+9) + 6x = x(x+9)
6x + 54 + 6x = x^2 + 9x
x^2 -3x - 54 = 0
Factor:
x^2 -9x+6x - 54 = 0
x(x-9) + 6(x-9) = 0
(x-9)(x+6) = 0
Positive solution:
x = 9 (time for Juanita to do the job alone)
x+9 = 18 (time for Rick to do the job alone)
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Cheers,
Stan H.
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