Question 149044: 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 2 solutions by ptaylor, Electrified_Levi:
Answer by ptaylor(2198)   (Show Source):
You can put this solution on YOUR website! Let x=amount of time it will it take all 3 of them working together to mix the 20 drinks. {Our final equation will be of the form: Rate at which they mix drinks when working together (drinks/min) times x minutes equals 20 drinks}
Steven mixes at the rate of 4 drinks per minute
Sue mixes at the rate of 2 drinks per minute
Jack mixes at the rate of 20/15 or 4/3=1 1/3 drinks per minute
Together, they mix at the rate of 4 + 2 + (1 1/3)=7 1/3 drinks per minute
So, our equation to solve is:
(7 1/3)*x=20 divide each side by 7 1/3
x=2.73 minutes---------------------amount of time it will it take all 3 of them working together to mix the 20 drinks
CK
2.73*7.33=20
20.019~~~~20
Hope this helps---ptaylor
Answer by Electrified_Levi(103)  (Show Source):
You can put this solution on YOUR website! Hi, Hope I can help,
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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?
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First, you have to make sure that all the measurements are the same(if it says Bob can do it in 5 hours, and John can do it in 45 minutes, you have to convert minutes to hours, or hours to minutes) They are all the same in our problem
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This is the way I usually solve these types of problems
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You are trying to find out how long it will take them, doing the job together.
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Here is the formula I use
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 ( If there was another you would add
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 , and so on)
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The "x" is how long it will take for all of them together to get the job done
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If you add the fractions together it will equal 1 job
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We can now replace the bottom numbers(denominators) with "5","10","15"( that's how long it takes each person)
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We can now solve for "x", we will multiply everything by "30" to get rid of the denominators, and fractions
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It will become
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We will add the left side
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We can divide each side by "11"
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If they all work together they can get the job done in 2  minutes, we can check by replacing "x" with "2 " or " " in our equation
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They can get the job done in minutes, or 2 minutes
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Hope I helped, Levi
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