3 women and 18 children together take 2 days to complete a piece of work. How many days will 9 children alone take to complete the piece of work if 6 women alone can complete the piece of work in 3 days?

6 women complete work in 3 days, so 1 woman's 1-day work = 1/(6×3) = 1/18. Thus 3 women's 1-day work = 3/18 = 1/6. The 3 women + 18 children team completes the work in 2 days, so their 1-day work = 1/2. Therefore 18 children's 1-day work = 1/2 - 1/6 = 1/3. So 9 children's 1-day work = 1/6, meaning 9 children take 6 days. This is a classic work-rate problem using reciprocals.