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 135070: 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?
Found 3 solutions by solver91311, ptaylor, ankor@dixie-net.com:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
Steve: 20 drinks in 5 minutes => 20%2F5=4 drinks per minute

Sue: 20 drinks in 10 minutes => 2 drinks per minute

Jack 20 drinks in 15 minutes => 4/3 drinks per minute

Together they mix 4 + 2 + 4/3 = 12/3 + 6/3 + 4/3 = 22/3 drinks per minute

20%2F%2822%2F3%29=60%2F22=30%2F11 minutes, very roughly a little less than 2 and 3/4 minutes.

Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=amount of time it takes all three working together to mix 20 drinks
Steven mixes at the rate of 1/5 of the job ( mixing 20 drinks) per minute
Sue mixes at the rate of 1/10 of the job per minute
Jack mixes at the rate of 1/15 of the job per minute
Together they mix at the rate of 1/5 + 1/10 + 1/15 multiply each term by 30/30
6/30 + 3/30 +2/30=11/30
So, together they mix at the rate of 11/30 of the job per minute. Our equation to solve then is:
(11/30)x=1 (1 job or 20 drinks, that is)
multiply each side by 30
11x=30 divide each side by 11
x=2.727272727--- minutes

Hope this helps---ptaylor

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, how much time will it take all 3 of them working together to mix the 20 drinks?
:
Here is another method, which I think is simpler.
:
Let t = time (in min) required when they all work together
:
Let the completed job = 1; (the mixing of 20 drinks)
:
A simple shared work equation:
t%2F5 + t%2F10 + t%2F15 = 1
:
Multiplying the equation by 30 gets rid of the denominators:
6t + 3t + 2t = 30
:
11t = 20
:
t = 30%2F11
:
t = 2.727 min
:
:
Check:
2.727%2F5 + 2.727%2F10 + 2.727%2F15 =
.545 + .272 + .182 = .99 ~ 1
:
Sorry I got my numbers wrong the 1st time.