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Math Help - basic algebra

  1. #1
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    Exclamation basic algebra

    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?
    is there a rule for this??!
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  2. #2
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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?
    is there a rule for this??!"

    Well Steven is mixing 20/5= 4 drinks per minute.
    Sue is mixing 20/10=2 drinks per minute.
    Jack is mixing 20/15=4/3 drinks per minute.

    So in 1 minute (60 seconds), the 3 of them can mix 4+2+(4/3)=(22/3) drinks

    So:

    60 seconds - 22/3 drinks
    90/11 seconds - 1 drink
    (90/11)*20 seconds = 20 drinks

    So the answer is 163.6 seconds.

    There is probably a quicker way though
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  3. #3
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    Since the three of them mix drinks at a rate of 22/3 drinks per minute . . .

    ....20 drinks
    --------------.....= 30/11 minutes or 2.73 minutes or 163.6 seconds
    (22/3 drinks/min)
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  4. #4
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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?
    is there a rule for this??!

    Working together problems use this format:

    Time together / time alone + time tog/ time alone = 1 [full job]
    x/5 + x/10 + x/15 = 1 Multiply by common denom (30) to clear the fractions -->
    6x + 3x + 2x = 30
    11x = 30
    x = 30/11

    Here's another approach: If they all work until the slowest one is finished (15 mins), how many drinks will they have?
    60 + 30 + 20 = 110 in 15 mins
    But we only want 20 drinks, so
    110/ 20 = 15/x
    110x = 20*15
    x = 30/11
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