To solve the problem, we can start by calculating the total amount of work needed to complete the task in terms of man-days.
Given that 9 men can complete the task in 15 days, the total work can be calculated as follows:
\[ \text{Total work} = \text{Number of men} \times \text{Number of days} = 9 \text{ men} \times 15 \text{ days} = 135 \text{ man-days} \]
Now, if we employ 3 additional men, the total number of men working on the task becomes:
\[ 9 \text{ men} + 3 \text{ men} = 12 \text{ men} \]
Next, we need to determine how many days it would take for 12 men to complete the same task. We can set up the equation using the total amount of work we calculated earlier:
\[ \text{Number of days} = \frac{\text{Total work}}{\text{Number of men}} = \frac{135 \text{ man-days}}{12 \text{ men}} \]
Calculating this gives:
\[ \text{Number of days} = \frac{135}{12} = 11.25 \text{ days} \]
Thus, with 3 additional men employed, it would take approximately 11.25 days to complete the task.
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