SOLUTION: 9. 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 togethe

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Question 655171: 9. 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?
I have tried averaging drink times. How long it takes for each person to make a drink and a few other things. I have not done word problems for 25 years so I am sure there is an easy way to solve it but my brain can not think of it. Thanks in advance for your help, I greatly appreciate!
Found 2 solutions by nerdybill, ankor@dixie-net.com:
Answer by nerdybill(7384) (Show Source):
You can put this solution on YOUR website!
9. 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?
.
This is considered a "rate" problem.
Steven's "rate" is 20 drinks per 5 mins = 20/5 = 4 drinks per minute
Sue's rate is 20 drinks per 10 mins = 20/10 = 2 drinks per minute
Jack's rate is 20 drinks per 15 mins = 20/15 = 4/3 = 4 drinks per 3 minutes
.
Let x= time for all three to make 20 drinks
then
x(4/1 + 2/1 + 4/3) = 20
multiplying both sides by 3:
x(12 + 6 + 4) = 60
x(22) = 60
x = 60/22
x = 2.73 minutes
or
x = 2 minutes and 44 seconds

Answer by ankor@dixie-net.com(22740) (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?
:
There is an easy way
Let the completed job = 1 (the mixing of 20 drinks)
:
Let t = time needed when all 3 work together
Each will do a fraction of the job, the three fractions add up to 1
+ + = 1
multiply by 60 to clear the denominators, results:
12t + 6t + 4t = 60
22t = 60
t = 60/22
t = 2.72 minutes working together or 2 + .72(60) = 2 min 43.6 sec