Final answer:
To determine the number of days 4 men and 4 women need to complete the work, we solve for the work rates of men and women using the equations formed from the given work completion times. Then we use the combined work rate of 4 men and 4 women to find the total number of days required.
Step-by-step explanation:
To find the number of days needed by 4 men and 4 women to complete the work, we first need to establish the work rates of men and women separately based on the information given in the question.
Let's assume the work rate of a man per day is m and the work rate of a woman per day is w. From the given information,
- 1 man and 2 women can complete the work in 10 days, so the equation is 10(m + 2w) = 1 work.
- 2 men and 3 women can complete the work in 6 days, so the equation is 6(2m + 3w) = 1 work.
Solving these two equations simultaneously gives us the individual rates of work for a man and a woman. Once we have m and w, we can calculate the rate at which 4 men and 4 women would complete the same work:
Rate of 4 men and 4 women = 4m + 4w
The number of days needed is the reciprocal of this rate:
Days needed = 1 / (4m + 4w)
Substituting back the values of m and w we found earlier, we can determine the actual number of days needed for 4 men and 4 women to complete the work.