SOLUTION: 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

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
RELATED QUESTIONS
If BIll can clean the garage in 4 hours and John can clean the same garage in 3 hours,... (answered by stanbon)

Working together, Sarah and Heidi can clean the garage in 6 hours. If they work alone, it (answered by richwmiller)

Working together, Sarah and Heidi can clean the garage in 6 hours. If they work alone, it (answered by josmiceli)

A can clean a room in 5 hours. After A worked alone for 2 hours, B joined him. Together... (answered by ikleyn,Edwin McCravy)

Dan can clean the garage in 6 hours. Bea can do the same job in 8 hours. if they work... (answered by Alan3354)

It takes Brenda 15 hours to clean an attic. Danielle can clean the same attic in 13... (answered by josmiceli,Edwin McCravy)

Rob takes 9 hours to clean the attic. Huong can clean the same attic in 15 hours. How (answered by ikleyn,josmiceli)

DON CLEAN THE HOUSE IN 3 HOURS. LISA CLEANED IT IN 8 HOURS. HOW LONG WILL IT TAKE THEM TO (answered by ankor@dixie-net.com)

Phillip can clean a garage in 9 hours less time than his brother Chris. Working together, (answered by richwmiller)