SOLUTION: John can paint a house in 6 days. It would take Tom 9 days to do the same work. If John works alone for 2 days and then is joined by Tom, how much total time is needed for painting

Algebra ->  Rate-of-work-word-problems -> SOLUTION: John can paint a house in 6 days. It would take Tom 9 days to do the same work. If John works alone for 2 days and then is joined by Tom, how much total time is needed for painting      Log On


   

Question 952894: John can paint a house in 6 days. It would take Tom 9 days to do the same work. If John works alone for 2 days and then is joined by Tom, how much total time is needed for painting the entire house?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
John can paint a house in 6 days.
It would take Tom 9 days to do the same work.
If John works alone for 2 days and then is joined by Tom, how much total time is needed for painting the entire house?
:
t = total time required to paint the house (the time worked by John)
then
(t-2) = time worked by Tom
:
The the completed job = 1 (a painted house)
:
A shared work equation, each will do a fraction of the job, the two fractions add up to 1
t%2F6 + %28%28t-2%29%29%2F9 = 1
multiply equation by 18 to clear the denominators
18*t%2F6 + 18*%28%28t-2%29%29%2F9 = 18
Cancel the denominators
3t + 2(t-2) = 18
3t + 2t - 4 = 18
5t = 18 + 4
5t = 22
t = 22/5
t = 4.4 days to paint the house