Question 376475
It takes Joe 12 hours to paint a fence, but Bob can do the job in 9 hours. How long does Joe work by himself before being joined by Sam if they finish the job working 3 hours together? 
Let x = number of hours Joe works by himself
then
"portion of work by Joe" + "work together" = "total job"
x/12 + 3(1/12 + 1/9) = 1
x/12 + (1/4 + 1/3) = 1
multiplying both sides by 12:
x + (3 + 4) = 12
x + 7 = 12
x = 5 hours