To determine how many days it would take for 18 women to complete a task that 10 men can complete in 24 days, we need to follow a systematic approach.
### Step-by-step Solution:
1. Calculate the total amount of work in man-days:
- 10 men can complete the task in 24 days.
- Hence, the total work is:
[tex]\[
\text{Total work} = 10 \text{ men} \times 24 \text{ days} = 240 \text{ man-days}
\][/tex]
2. Determine the equivalent time one woman takes compared to one man:
- One woman takes 20% more time than one man to complete the same task.
- If one man takes 1 unit of time, one woman takes [tex]\(1.20\)[/tex] units of time.
3. Convert work to woman-days:
- Since one woman takes 1.20 times the amount of time that one man does, the work in woman-days is increased by the same factor.
- Therefore, the total work in woman-days is:
[tex]\[
\text{Total work in woman-days} = 240 \text{ man-days} \times 1.20 = 288 \text{ woman-days}
\][/tex]
4. Calculate the number of days 18 women would take to complete the task:
- To find the number of days required, we divide the total woman-days by the number of women.
- Hence, the number of days required is:
[tex]\[
\text{Days} = \frac{288 \text{ woman-days}}{18 \text{ women}} = 16 \text{ days}
\][/tex]
### Conclusion:
Thus, it would take 18 women [tex]\(16\)[/tex] days to complete the task.
