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Question 4564: 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 rapaljer(4671)   (Show Source):
You can put this solution on YOUR website! In this problem, everyone is measured on the time it takes to mix the same number of drinks, which is 20. It doesn't matter how many drinks they are mixing as long as it is the same for all of them. You can therefore, write this as "THE" drinks instead of 20 drinks, it will be the same, no matter how many that is.
Since Stephen can mix THE drinks in 5 minutes, then in 1 minute, he can mix  of them.
Since Sue can mix THE drinks in 10 minutes, then in 1 minute, she can mix  of them.
Likewise, since Jack can mix THE drinks in 15 minutes, in 1 minute, he can mix  of them.
Let x = time it takes them to mix THE drinks working together, and  is the part of THE drinks that they can mix together in 1 minute.
The equation is 
Multiply both sides of the equation by the Least Common Denominator, which is 30x:
R^2 at SCC
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