6 men and 8 women can complete a job in 18 days. 9 men and 4 women can complete the same job in 18 days. In how many days will 9 men and 12 women complete a job that is twice as big as the initial job?

6M + 8W in 18 days and 9M + 4W in 18 days. This implies 6M + 8W = 9M + 4W, so 3M = 4W or M = 4/3 W. Substitute into first: 6(4/3 W) + 8W = 16W. 16W take 18 days. We want 9M + 12W = 9(4/3 W) + 12W = 12W + 12W = 24W. For the same job, 16W * 18 days = 24W * D, so D = 12 days. Since the job is twice as big, D = 12 * 2 = 24 days.