SOLUTION: If Steven can mix 20 drinks in 5 min, Sue can mix 20 drinks in 10 min, and Jack can mix drinks in 15 min. How much time will it take all 3 of them working together to mix the 20 dr

Algebra ->  Sequences-and-series -> SOLUTION: If Steven can mix 20 drinks in 5 min, Sue can mix 20 drinks in 10 min, and Jack can mix drinks in 15 min. How much time will it take all 3 of them working together to mix the 20 dr      Log On


   

Question 160195: If Steven can mix 20 drinks in 5 min, Sue can mix 20 drinks in 10 min, and Jack can mix drinks in 15 min. How much time will it take all 3 of them working together to mix the 20 drinks?
The answer is 2 min and 44 seconds, but I don't know how.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
If Steven can mix 20 drinks in 5 min, Sue can mix 20 drinks in 10 min, and
Jack can mix 20 drinks in 15 min. How much time will it take all 3 of them
working together to mix the 20 drinks?
:
Let t = time required when they all work together
:
Let the completed job = 1 (the mixing of 20 drinks)
:
Each will do a fraction of the job, which added together, will = 1
:
t%2F5 + t%2F10 + t%2F15 = 1
:
Clear the denominators, multiply equation by 30, results:
6t + 3t + 2t = 30
:
11t = 30
t = 30%2F11
t = 2.727 min or about 2 min 43.6 sec. all working together
:
:
Check solution on calc:
2.7%2F5 + 2.7%2F10 + 2.7%2F15 =
.54 + .27 + .18 = .99 ~ 1