# SOLUTION: 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

Algebra ->  Algebra  -> Rate-of-work-word-problems -> SOLUTION: 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      Log On

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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(2048)   (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