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?

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