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

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Question 529579: 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 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 minutes,
Sue can mix 20 drinks in 10 minutes,
and Jack can mix 20 drinks in 15 minutes,
ow much time will it take all 3 of them working together to mix the 20 drinks?
:
There is an easy way to do this.
:
Let t = time required to do the job when they all work together
Let the completed job = 1 (the mixing of 20 drinks)
:
t%2F5 + t%2F10 + t%2F15 = 1
multiply by 30, the LCM of the 3 denominators
30*t%2F5 + 30t%2F10 + 30*t%2F15 = 30(1)
Cancel out the denominators and you have
6t + 3t + 2t = 30
11t = 30
t = 30%2F11
t = 2.73 minutes or 2 + .73(60) = 2 min 43.6 seconds
:
:
Check this
2.73%2F5 + 2.73%2F10 + 2.73%2F15 =
.546 + .273 + .182 = 1.00; confirms our solution of 2.73 min