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Math Help - Please help. Basic problem of fractions/ percentages

  1. #1
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    Please help. Basic problem of fractions/ percentages

    If 2 workmen ( Jack and Jill ) split profit in a week on a 60/40 basis (in favour of Jill) So long as they work the same amount of time..

    What would the split be if Jack worked 2.5 days in a week and Jill only worked 2?
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  2. #2
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    Re: Please help. Basic problem of fractions/ percentages

    you haven't given us any rule for splitting the profit when they don't work the same amount of time.
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  3. #3
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    Re: Please help. Basic problem of fractions/ percentages

    I think thats what needs to be worked out.
    So if the usual split had been 50/50 then the profit would be divided by 4.5 then times by 2.5 to find jacks wages and the rest being 2(profit/4.5) would be jills
    but if the profit is not usually split equally ( in this case 60/40 ) what would the formula look like for the 2.5 and 2 day week?
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  4. #4
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    Re: Please help. Basic problem of fractions/ percentages

    Hi, I know this question is old, but I thought I'd try to answer it. This is my first post to the forum.

    I'm assuming that the reason for the profit split is that, for each hour they work, Jill produces 50% more profit than Jack (eg Jill 6, Jack 4). So the 60/40 split is equitable for their work. (If this assumption is wrong then so is my answer below!). I'll call Jack's profitability rate P, so Jill's is 3P/2

    So, given the 2.5 hours to Jack and the 2 hours to Jill, the profit produced would be 2.5xP and Jill's would be 3xP. The fractional split would then be 3P/5.5P to Jill and 2.5P/5.5P to Jack, or simplified 6/11ths to Jill and 5/11ths to Jack.

    In the general case where Jack works K hours and Jill works L hours, the proportional split is 2K/(2K+3L) to Jack and 3L/(2K+3L) to Jill.

    Hope this is still useful ghend after all these months.
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  5. #5
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    Re: Please help. Basic problem of fractions/ percentages

    Here's what I would do. Let's say the profit was "P". Both Jack and Jill worked 2 hour which is 4/4.5= 40/45= 8/9 of the job so assign 8/9 of the profit, (8/9)P, to that. Since Jill gets 60 percent of the profit, her take from those 2 hours is (6/10)(8/9)P= (3/5)(8/9)P= (8/15)P and Jack's is (4/10)(8/9)P= (2/5)(8/9)P= (16/45)P. As a check, that is a total of (8/15)P+ (16/45)P= ((24+ 16)/45)P= (40/45)P= (8/9)P as said. And since Jack worked alone for the last 1/2 hour, I would give him the remaining (1/9)P. So I would give Jill 8/15 of the profit and Jack ((1/9)+ (16/45)P)= ((5+ 16)/45)P= (21/45)P= (7/15)P or 7/15 of the profit.

    Notice that 8/15 and 7/15 are 0.53333... and 0.46666... as opposed to KingStephen6029's 6/11= 0.545454... and 5/11= 0.454545.... He gives just slightly more to Jill and slightly less to Jack than I do. As romsek said, back in July, the answer will depend upon what assumptions you make.
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  6. #6
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    Re: Please help. Basic problem of fractions/ percentages

    Thank you all for posting these replies. Its been a long time but still this has been most helpful.

    The reason for the profit split is that, for each hour they work, Jill produces 50% more profit than Jack as KingStephen assumes.

    Therefore I will use your sugestion as it seems most simple and fair based on this assumption

    Thanks again
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  7. #7
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    Re: Please help. Basic problem of fractions/ percentages

    Then 6:5 in favor of Jill.
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