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Question 272217: X can clean the garage in half the time it takes B. If they cleaned it together in 3 hours, how many hours would it take form A to clean the garage all by himself?
(A) 6 (B) 5.5 (C) 5 (D) 4.5 (E) 4
Answer by ptaylor(2198)   (Show Source):
You can put this solution on YOUR website! Let x=amount of time it takes B to clean the garage
Then x/2=amount of time it takes A to clean the garage
B works at the rate of 1/x of the garage per hour
A works at the rate of 1/(x/2) or 2/x of the garage per hour
Together they clean at the rate of 1/x + 2/x of the garage per hour
But we are told that together they can clean the garage in 3 hours, so together they work at the rate of 1/3 of the garage per hour, so our equation to solve is:
1/x+2/x=1/3
3/x=1/3 multiply each term by 3x
9=x
x=9 hours ----amount of time it takes B to clean the garage
x/2=9/2=4.5 hours------amount of time it takes A to clean the garage
CK
In 3 hours, B cleans (1/9)(3)=3/9 of the garage
In 3 hours, A cleans (2/9)(3)=6/9 of the garage
And 3/9+6/9=9/9 or 1 garage
Hope this helps---ptaylor
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