SOLUTION: 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 toge

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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?
I've tried setting up a system of equations, but am not having much luck. I think that the first equation is x/12 + y/9 = 1, with x being the number of hours Joe works and y the number of hours Bob works, but I can't figure out the second equation.
Found 2 solutions by nerdybill, ankor@dixie-net.com:
Answer by nerdybill(7384) (Show Source):
You can put this solution on YOUR website!
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

Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
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?
:
We can do it with one equation, but I'm going to ignore Sam's contribution here
:
Let t = time Joe worked by himself
and
Bob works 3 hrs
and
(t+3) = total time Joe worked
:
Let the completed job = 1
:
+ = 1
Multiply by 36, results:
3(t+3) + 4(3) = 36
3t + 9 + 12 = 36
3t + 21 = 36
3t = 36 - 21
3t = 15
t =
t = 5 hrs Joe works by himself
;
:
Let's see if that is true (Joe works 8 hrs total),
8/12 + 1/3 = 1