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? 
:
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
:
{{{((t+3))/12}}} + {{{3/9}}} = 1
Multiply by 36, results:
3(t+3) + 4(3) = 36
3t + 9 + 12 = 36
3t + 21 = 36
3t = 36 - 21
3t = 15
t = {{{15/3}}}
t = 5 hrs Joe works by himself
;
:
Let's see if that is true (Joe works 8 hrs total),
8/12 + 1/3 = 1