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?

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