Question 149044
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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{{{ (x/(how long it takes for person(1)))+(x/(how long it takes for person(2)))+(x/(how long it takes for person(3))) = 1 }}} ( If there was another you would add
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 {{{(x/(how long it takes for person(4))) }}}, 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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{{{ (x/5)+(x/10)+(x/15) = 1 }}}
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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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{{{ (30)(x/5)+(30)(x/10)+(30)(x/15) = (30)1 }}}
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It will become
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{{{ 6x + 3x + 2x = 30 }}}
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We will add the left side
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{{{ 11x = 30 }}}
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We can divide each side by "11"
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{{{ 11x/11 = 30/11 }}}
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{{{ x = 30/11 }}}
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If they all work together they can get the job done in 2 {{{ 8/11 }}} minutes, we can check by replacing "x" with "2 {{{ 8/11 }}}" or "{{{ 30/11 }}}"  in our equation
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{{{ ((30/11)/5)+((30/11)/10)+((30/11)/15) = 1 }}}
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{{{ (6/11)+(3/11)+(2/11) = 1 }}}
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{{{ 11/11 = 1 }}}
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{{{ 1 = 1 }}}
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They can get the job done in {{{ 30/11 }}} minutes, or 2 {{{ 8/11 }}} minutes
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Hope I helped, Levi