SOLUTION: Derek can wash and was a car in exactly 2 hours. Allison can do the same job in exactly 5 hours. How long will it take both of them working together (at their usual rates) to wash

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Derek can wash and was a car in exactly 2 hours. Allison can do the same job in exactly 5 hours. How long will it take both of them working together (at their usual rates) to wash       Log On


   

Question 876901: Derek can wash and was a car in exactly 2 hours. Allison can do the same job in exactly 5 hours. How long will it take both of them working together (at their usual rates) to wash and wax the car.
Answer by LinnW(1048) About Me  (Show Source):
You can put this solution on YOUR website!
Derek's rate is 1/2 car per hour
Allison's rate is 1/5 car per hour
Set t = time to complete
(1/2 + 1/5)t = 1
%28+%281%2F2%29%2A%285%2F5%29+%2B+%281%2F5%29%2A%282%2F2%29%29+t+=+1
%28+%285%2B2%29%2F10%29+t+=+1
%28+7%2F10%29+t+=+1
multiply each side by 10/7
t+=+1%2A%2810%2F7%29
t = 1 3/7 hours
checking
(1/2 + 1/5)(10/7) = 1
See
http://www.wolframalpha.com/input/?i=%281%2F2+%2B+1%2F5%29%2810%2F7%29