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Math Help - algebra word problems

  1. #1
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    Unhappy algebra word problems

    in a factory pf two different machines, A and B, are used to fill bottles. when the machines work together they fill the botlles in 2 hours. machine A works twice as fast as machine B. how long does it take machine B to fill the bottles when it works alone?
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  2. #2
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    Quote Originally Posted by zorodzai View Post
    in a factory pf two different machines, A and B, are used to fill bottles. when the machines work together they fill the botlles in 2 hours. machine A works twice as fast as machine B. how long does it take machine B to fill the bottles when it works alone?
    When two people or machines, etc., work together, their speeds add. Let T be the time, in hours, it takes T hours for B to fill the bottles so its speed is 1/T (jobs/hour). Since A works twice as fast, its speed it 2/T. Working together they have speed 1/T+ 2/T= 3/T. Since it took them 2 two hours to do the job together we know their speed together is really 1/2 job/hour.

    3/T= 1/2. Solve for T.

    (This time I got in before earboth!)
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  3. #3
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    Quote Originally Posted by zorodzai View Post
    in a factory pf two different machines, A and B, are used to fill bottles. when the machines work together they fill the botlles in 2 hours. machine A works twice as fast as machine B. how long does it take machine B to fill the bottles when it works alone?
    Time together = 2 hours

    Time alone:
    A = B / 2

    B = B

    You use this equation (time together over time alone is equal to 1 work)


    \frac {2}{A} + \frac{2}{B} = 1

    \frac {4}{B} + \frac{2}{B} = 1

    \frac {4}{B} + \frac{2}{B} = 1 ] B

    4 + 2 = B

    B = 6 hours

    A = 3 hours
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