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Question 350831: Four men and three women can do a job in 6 days. When five men and six women work on the same job, the work gets completed in 4 days. How long will a woman take to do the job, if she works alone on it?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Fact: rate + rate = together rate
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Let "m" be the men's rate and "w" be the woman's rate.
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Four men and three women can do a job in 6 days.
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4m+3w = 1/6
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When five men and six women work on the same job, the work gets completed in 4 days.
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5m+6w= 1/4
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Multiply thru 1st equation by 2 to get:
8m + 6w = 1/3
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Subtract 2nd from latter to get:
3m = (1/3)-(1/4)
3m = 1/12
m = 1/36
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Solve for "w" using 4m+3w = 1/6
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4(1/36) + 3w = 6/36
3w = 2/36
w = 1/54
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How long will a woman take to do the job, if she works alone on it?
Answer: 54 days
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Cheers,
Stan H.
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