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?

Algebra ->  Rate-of-work-word-problems -> 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?      Log On


   

Question 311811: 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?
Answer by ankor@dixie-net.com(22740) About Me  (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?
:
Let t = time for J to do it alone
then
(t+9) = time for R to do it alone
:
Let the completed job = 1
:
A shared work equation:
6%2Ft + 6%2F%28t%2B9%29 = 1
Multiply equation by t(t+9), results
6(t+9) + 6t = t(t+9)
:
6t + 54 + 6t = t^2 + 9t
combine on the right
0 = t^2 + 9t - 12t - 54
:
t^2 - 3t - 54 = 0
Factor
(t-9)(t+6) = 0
positive solution
t = 9 hrs J, alone
then
9 + 9 = 18 hrs R alone
:
:
Check solution
6/9 + 6/18 = 1
:
Note: Rick only has one arm