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Math Help - Time and Work hard problem

  1. #1
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    Time and Work hard problem

    I am finding this really hard to do
    A,B and C can complete a work in 12,15 an 20 days respectively.
    • how long will it take to do the work together?
    • If they start the work together,and C leaves for 2 days,then how long will it take for A and B to do the work together?


    I did the first part and i got 5.
    Please help me
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  2. #2
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    Re: Time and Work hard problem

    When people (or machines, etc) work together, their rates add.
    "A,B and C can complete a work in 12,15 an 20 days respectively."
    So A's rate of work is "one job in 12 days" or 1/12 job per day. Similarly, B's rate is 1/15 job per day and C's is 1/20 job per day. Together they can do 1/12+ 1/15+ 1/20 job per day. 12= 4(3), 15= 5(3) and 20= 4(5) so the least common denominator is 3(4)(5)= 60. 1/12+ 1/15+ 1/20= 5/60+ 4/60+ 3/60= 12/60= 1/5 job per day. So you were right- at 1/5 job per day, they will complete the job in 5 days.

    "If they start the work together,and C leaves for 2 days,then how long will it take for A and B to do the work together?"
    So all three, A, B, and C, work for three days, at 1/5 job per day and so compete 3/5 of the job, leaving 2/5 of the job still to be done.
    A and B working together, without C, have rate 1/12+ 1/15= 5/60+ 4/60= 9/60= 3/20 job per day.
    At 3/20 job per day, how long will it take them to do 2/5 job?
    Last edited by HallsofIvy; September 20th 2012 at 09:47 AM.
    Thanks from NormalKid
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  3. #3
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    Re: Time and Work hard problem

    Thank You Sir
    BTW it is 2/5 right? you wrote 2/4...........
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  4. #4
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    Re: Time and Work hard problem

    Yes, thanks, "2/4" was a typo.
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  5. #5
    MHF Contributor MarkFL's Avatar
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    Re: Time and Work hard problem

    A similar method is to observe that lcm(12,15,20) = 60, so in 60 days:

    A can do 5 tasks

    B can do 4 tasks

    C can do 3 tasks

    for a total of 12 tasks done combined in 60 days, or 1 task every 5 days.
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  6. #6
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    Re: Time and Work hard problem

    Thank you Mate
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