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Question 496727: If Tom, George and Mario work together, they can paint a 600 ft2 room in 4 hours. When only George and Mario work together, it takes 8 hours to paint the room. Tom and George, working together, take 6 hours to paint the room. How long would it take Tom to paint the room alone?
a. 8 hours c. 3 hours
b. 23 hours d. 4 hours
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! If Tom, George and Mario work together, they can paint a 600 ft2 room in 4 hours.
When only George and Mario work together, it takes 8 hours to paint the room.
Tom and George, working together, take 6 hours to paint the room.
How long would it take Tom to paint the room alone?
:
Let the completed job = 1, (a painted room)
Let t = To alone
let g = George alone
let m = Mario alone
:
Write a shared work equation for each statement:
:
"Tom, George and Mario work together, they can paint a room in 4 hours."
 +  +  = 1
:
"When only George and Mario work together, it takes 8 hours to paint the room."
 +  = 1
:
"Tom and George, working together, take 6 hours to paint the room."
 +  = 1
:
Use elimination here, multiply the 1st equation by 6, the 2nd equation by 3
 +  +  = 6
 + + = 3
-------------------------------------------subtraction eliminates g and m
+ 0 + 0 = 3
3t = 24
t = 24/3
t = 8 hrs for Tom working alone
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