SOLUTION: Arthur can do a job in 30 minutes, Bonnie can do it in 40 minutes, and Claire can do it in 60 minutes. How long will it take them if they work together?

Question 133568: Arthur can do a job in 30 minutes, Bonnie can do it in 40 minutes, and Claire can do it in 60 minutes. How long will it take them if they work together?
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
Arthur can do a job in 30 minutes, Bonnie can do it in 40 minutes, and Claire can do it in 60 minutes. How long will it take them if they work together?
Let x=amount of time it takes them working together
Arthur works at the rate of 1/30 of the job per min
Bonnie works at the rate of 1/40 of the job per min
Claire works at the rate of 1/60 of the job per min

Together they work at the rate of 1/30+ 1/40 +1/60 of the job per min. This equals
1/30 + 1/40 + 1/60= 4/120 + 3/120 + 2/120= 9/120 of the job per min
Now, our equation to solve is:
(9/120)x=1 (1 job, that is) multiply each side by 120
9x=120 divide both sides by 9
x=13 1/3 min----------------time it takes them working together

Hope this helps---ptaylor
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