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Math Help - Complex Work Problem.. Suggestions ??

  1. #1
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    Question Complex Work Problem.. Suggestions ??

    In one half the time Abby can produce three times as much work as Beth. Beth can do in twice the time 1/3 as much work as carol. If carol does a job in one hour , how many hours will it take Abby to do the same job. ?
    The answer is 1 however i am getting 0.75. Could anyone tell me where i am going wrong

    Solution:
    Beth:
    Beth thus
    1/3 of work in 2 hours
    so for one job it takes 6 hours.

    Abby:
    6 * (2/3) = 4 hours.
    So in 4 hours Abby does 3 jobs
    so 1 job takes 3/4 hours.
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  2. #2
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    Re: Complex Work Problem.. Suggestions ??

    Replace the question marks in the line below.

    Beth : 1 job in 6 hours.
    Abby : ? jobs in ? hours.
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  3. #3
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    Re: Complex Work Problem.. Suggestions ??

    Abby : ? jobs in ? hours.
    Abby : 1 jobs in 3/4 hours.
    Dont really get it... 3/4 isnt the answer
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  4. #4
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    Re: Complex Work Problem.. Suggestions ??

    Half the time three times the work.
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  5. #5
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    Re: Complex Work Problem.. Suggestions ??

    @BObP.
    Okay so the answer comes up with half the time. But the question states one half (1 .1/2) which i actually used or maybe i was wrong. So my solution is correct , of i used half instead of one and a half.
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  6. #6
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    Re: Complex Work Problem.. Suggestions ??

    In one half the time Abby can produce three times as much work as Beth. Beth can do in twice the time 1/3 as much work as carol. If carol does a job in one hour , how many hours will it take Abby to do the same job. ?
    carol does (1 job)/(1 hr)

    beth does (1/3 job)/(2 hrs)

    abby does (3 * 1/3)/(1/2 * 2) = (1 job)/(1 hr)
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  7. #7
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    Re: Complex Work Problem.. Suggestions ??

    Yet another variation:
    "carol does a job in one hour"
    "Beth can do in twice the time 1/3 as much work as carol."

    So in 2 hours Beth does 1/3 the job. It would take her 6 hours to do the job.

    "In one half the time Abby can produce three times as much work as Beth."

    So in 3 hours, Abby can do the job three times. She can do the job once in one hour, just like Abbey.

    From a purely "mathematical" point of view "twice the time" and "one half the time" cancel while "1/3 as much work" and "three times as much work" cancel.

    Your error was in converting "In one half the time Abby can produce three times as much work as Beth." into "2/3" Beth's time per job. In fact it should be "1/2 Beth's time" times "1/3 job"= "1/6 Beth's time per job".
    Last edited by HallsofIvy; June 2nd 2012 at 06:20 AM.
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  8. #8
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    Re: Complex Work Problem.. Suggestions ??

    first find how much beth can produce in 2 hours , which can be done by ratio and proportion.that would be 4/3. this is one third of how much carol produces in one hour. if this is one third carol can produce 4 units in one hour. so in order to gain 4 units beth shoud work 3 two hours which is also "6 hours"
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  9. #9
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    Re: Complex Work Problem.. Suggestions ??

    Let w= the work and t=the time
    Carol (w,t) Beth (1/3*w,2t) So Abbey (w,t) But for Carol t=1 So for Abbey t=1
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