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Question 494419: Abbie paints twice as fast as Beth and three times as fast as Cathie. If it takes them 60min to paint a living room with all three working together, how long would it take Abbie if she works alone?
Answer by ptaylor(2198)   (Show Source):
You can put this solution on YOUR website! Let x=amount of time it takes Abbie to paint the room
Then Abbie paints at the rate of 1/x rooms/min
2x=amount of time it takes Beth
Beth paints at the rate of 1/2x rooms/min
3x=amount of time it takes Cathy
And Cathy paints at the rate of 1/3x rooms/min
Together they paint at the rate of 1/x + 1/2x +1/3x=11/6x rooms/min
Now we are told that (11/6x)*60=1 (1 room, that is), or
x=110 min----------------Amount of time it takes Abbie
and 2*110=220 min--------Amount of time it takes Beth
3*110=330 min---------------Amount of time it takes Cathy
CK
In 60 min Abbie paints 60/110 of the room
Beth paints 60/220 of the room
Cathy paints 60/330 of the room
60/110 + 60/220 + 60/330=1 (1 room, that is)
6/11 + 6/22 + 6/33=1 multiply each term by 66
36+18+12=66
66=66
Hope this helps---ptaylor
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