5 men and 12 women finish a piece of work in 14 days, while 7 men and 6 women finish it in 20 days. In how many days will 18 women finish it?

Let a man's daily work be M and a woman's daily work be W. The given conditions set up the equations 5M + 12W = 1/14 and 7M + 6W = 1/20. Multiplying the second equation by 2 gives 14M + 12W = 1/10, and subtracting the first equation from this yields 9M = 1/10 - 1/14 = 4/140 = 1/35. Substituting M = 1/315 back into the first equation gives 12W = 1/14 - 1/63 = 7/126 = 1/18, meaning 18 women can complete 18 x (1/18) = 1 full work per day. Therefore, it will take 18 women exactly 12 days to finish the work.

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