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

Question 250479: Working together, Rick & Juanita can complete a job in 6 hr. It would take Rick 9 hr longer than Juanita to do the job alone. How long would it take Juanita alone?
Answer by dabanfield(803) (Show Source): You can put this solution on YOUR website!
Working together, Rick & Juanita can complete a job in 6 hr. It would take Rick 9 hr longer than Juanita to do the job alone. How long would it take Juanita alone?
Let T be the time it takes for the two working together to complete the job.
Then 1/T is the rate that Juanita can complete the job (i.e. jobs per hour).
Rick's rate then is 1/(T+9).
So for the combined rates have:
((1/T) + 1/(T+9)) * 6 = 1
Expanding we have:
6/T + 6/(T+9)= 1
Now you can solve this for T.
6*(T+9) + 6 * T = T^2 + 9*
T^2 -3*T -54 = 0
(T-9)*(T+6) = 0
T must be poisitive so
T = 9
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