Janet can do a job in 3 hours while garry can do the same job in 2 hours. if janet works for an hour before garry her, how long will it take them to finish the job together?

Here's my reasoning:  Janet works at the rate (1 job)/(3 hr), and works one hour before Gary steps in to help.  This means that Janet accomplishes 1/3 of the entire job by herself, leaving 2/3 of the job for the two of them to complete.

Thus, I write:

             2/3 job
= time required for the 2 to finish the job
 1 job      1 job
  +
  3 hr       2 hr

The LCD here is 3(2) = 6.  Mult. (2/3 job) by 6 results in 4 job, and
mult (1 job)/(3 hr) by 6 results in 2 job/hr, and mult (1 job)/(2 hr) by 6 results in 3 job /hr:

             4 job                   4 job
  = = (4/5) hr (answer)
    2 job/hr + 3 job/hr        5 job/hr