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?

I've tried it a couple different ways, but never get the right answer.  I know the answer is 9 hours...HELP!  :)

Make this chart:
                                     ACCOMPLISHMENT   RATE    TIME
Rick working alone                                                  
Juanita working alone                                              
Rick and Juanita working together                                

You are asked "How long would it take Juanita alone?"
We want to know Juanita's time alone to accomplish 1 job, so we
put X for her time and 1 for her accomplishment:

                                     ACCOMPLISHMENT   RATE    TIME
Rick working alone                                                
Juanita working alone                      1                    X
Rick and Juanita working together                                  

We are told that working together, Rick and Juanita can complete the
job in 6 hours.  That means together they made 1 accomplishment in
6 hours. So we put 1 for their acomplishment together and 6 for their
time together:


                                     ACCOMPLISHMENT   RATE    TIME
Rick working alone                                                
Juanita working alone                      1                    X
Rick and Juanita working together          1                    6

We are told that i would take Rick 9 hours longer than Juanita to do the job alone (1 accomplishment).  So we add 9 to Juanita's time, X, getting X+9.  
We put X+9 for Rick's time working alone, and 1 for his accomplishment:

                                     ACCOMPLISHMENT   RATE    TIME
Rick working alone                         1                   X+9
Juanita working alone                      1                    X
Rick and Juanita working together          1                    6

Next we use  to fill in the rates:


                                     ACCOMPLISHMENT   RATE    TIME
Rick working alone                         1         1/(X+9)   X+9
Juanita working alone                      1           1/X      X
Rick and Juanita working together          1           1/6      6

The equation is gotten from

Rick's rate alone + Juanita's rate alone = their rate together:



Can you solve that? If not, post again asking how.

Answer: X = 9, so it would take Juanita 9 hours.

Edwin