SOLUTION: Andrew can paint a fence in 7 hours and Diana can paint the same fence in 4 hours. How long would it take if Andrew and Diana work together? ( round answer to the nearest tenth and

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Andrew can paint a fence in 7 hours and Diana can paint the same fence in 4 hours. How long would it take if Andrew and Diana work together? ( round answer to the nearest tenth and      Log On


   

Question 969836: Andrew can paint a fence in 7 hours and Diana can paint the same fence in 4 hours. How long would it take if Andrew and Diana work together? ( round answer to the nearest tenth and label)
Found 2 solutions by ptaylor, Alan3354:
Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=time needed to paint fence when they work together
Then together they paint at the rate of 1/x fence per hour
Andrew paints at the rate of 1/7 fence per hour
Diana paints at the rate of 1/4 fence per hour
soooo
1/7 + 1/4=1/x multiply each term by 28x to get rid of fractions
4x+7x=28
11x=28
x=28/11 hrs (you can divide this out)
CK
In (28/11) hrs, Andrew paints(28/11)*(1/7)=4/11 of the fence
In (28/11) hrs, Diana paints (28/11)*(1/4)=7/11 of the fence
Those should add up to 1 fence and they do:)
Hope this helps----ptaylor

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
You might notice is the product/sum
----
7*4/(7+4)
= 28/11