SOLUTION: If Steven can mix 20 drinks in 5 minutes, Sue can mix 20 drinks in 10 minutes, and Jack can mix 20 drinks in 15 minutes, how much time will it take all 3 of them working together t

Algebra ->  Proportions -> SOLUTION: If Steven can mix 20 drinks in 5 minutes, Sue can mix 20 drinks in 10 minutes, and Jack can mix 20 drinks in 15 minutes, how much time will it take all 3 of them working together t      Log On


   

Question 457324: If Steven can mix 20 drinks in 5 minutes, Sue can mix 20 drinks in 10 minutes, and Jack can mix 20 drinks in 15 minutes, how much time will it take all 3 of them working together to mix the 20 drinks?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Since they all have to mix 20 drinks, I can call
20 drinks 1 job
Let t = time for all 3 working together
to mix 20 drinks
given:
Stephen's rate of working = (1 job) / (5 min)
Sue's rate = (1 job) / (10 min)
Jack's rate = (1 job) / (15 min)
Add their rates
+1%2F5+%2B+1%2F10+%2B+1%2F15+=+1%2Ft+
Multiply both sides by 30t
+6t+%2B+3t+%2B+2t+=+30+
+11t+=+30+
+t+=+2.73+
+.73%2A60+=+44+
It will take them 2 minutes and 44 seconds to mix 20 drinks