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Math Help - How long does it take 3 people to do a job?

  1. #1
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    Unhappy How long does it take 3 people to do a job?

    8. If Sam can do a job in 4 days that Lisa can do in 6 days and Tom can do in 2 days, how long would the job take if Sam, Lisa, and Tom worked together to complete it?

    A. 0.8 days
    B. 1.09 days
    C. 1.23 days
    D. 1.65 days
    E. 1.97 days

    So I know that the answer is B but I have no idea what formula I am supposed to use to actually get that answer....

    My friend and I did this but there has to be an easier way to do it, right?
    [03:57:51 p.m.] Blaze: sam can do 25% in a day...
    [03:58:13 p.m.] Blaze: lisa can do... 16.66%
    [03:58:23 p.m.] Blaze: and tom can do 50%....
    [03:58:59 p.m.] Blaze: in 1 day they can do 91.66%... right?
    which also means that together they accomplish about 3.82% an hour
    so far i've got 1 day 2 hours... let me go further
    [04:01:49 p.m.] Blaze: its also about 0.063% a minute
    [04:02:55 p.m.] Blaze: now im at 1 day 2 hours and 11 minutes and like 30 or so seconds


    So as you can see... this is not going well...

    ((DISCLAIMER: I am new to the site and have no idea what I am doing. xD So I am trying to follow the rules but I am not sure if I am putting this in the right section or giving the right amount of information or anything. Sorry if I am doing anything wrong ^^; ))
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  2. #2
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    Re: How long does it take 3 people to do a job?

    Quote Originally Posted by ButterflyGirl18 View Post
    8. If Sam can do a job in 4 days that Lisa can do in 6 days and Tom can do in 2 days, how long would the job take if Sam, Lisa, and Tom worked together to complete it?
    Change the units and you'll be done in a moment.

    Sam: 1 job in 4 days ==> 4 jobs in 1 day ==> 1/4 jobs per day
    Lisa: 1 job in 6 days ==> 6 jobs in 1 day ==> 1/6 jobs per day
    Tom: 1 job in 2 days ==> 2 jobs in 1 day ==> 1/2 jobs per day

    How many jobs can they complete in one day? 1/4 + 1/6 + 1/2

    Did we get there. yet?
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  3. #3
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    Re: How long does it take 3 people to do a job?

    But I am not looking for how many jobs they can do in one day I am looking for how many days it takes to do one job.

    If they can do 11/12 of the job in one day..... (1/4 + 1/6 + 1/2)
    How do I change it to find out how many days it takes to do the job?
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  4. #4
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    Re: How long does it take 3 people to do a job?

    Quote Originally Posted by ButterflyGirl18 View Post
    But I am not looking for how many jobs they can do in one day I am looking for how many days it takes to do one job.
    If they can do 11/12 of the job in one day..... (1/4 + 1/6 + 1/2)
    How do I change it to find out how many days it takes to do the job?
    \frac{12}{11}=?
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  5. #5
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    Re: How long does it take 3 people to do a job?

    (combined rates)(number of days) = 1 job

    \left(\frac{1 \, job}{4 \, days} + \frac{1 \, job}{6 \, days} + \frac{1 \, job}{2 \, days}\right) (t \, days) = 1 \, job \, done

    solve for t
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  6. #6
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    Re: How long does it take 3 people to do a job?

    So 11/12 * T = 1

    Ah! Ok! I get it now. =^.^= Thank you so much guys!
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