Final answer:
21 women would take the same number of days as 15 men, which is 21 days.
Step-by-step explanation:
To find the number of days of 6 hours each that 21 women would take to complete the work, we need to compare the work rates of men and women. According to the given information, 3 women do as much work as 2 men. So, the work rate of 2 men is equivalent to the work rate of 3 women.
Since the number of men is 15 and the number of women is 21, we can set up a proportion to solve for the number of days:
15 men * 8 hours/day = 21 women * 6 hours/day
Simplifying the equation, we get:
120 men-hours/day = 126 women-hours/day
To find the number of days for 21 women to complete the work, we can divide both sides of the equation by 126:
120 men-hours/day ÷ 126 women-hours/day = 21 women-days
Therefore, 21 women would take the same number of days to complete the work as 15 men, which is 21 days. So, the answer is option a. 21.