To solve this problem, we first need to determine how much work is involved in the job and how many men are required based on the time available.
1. **Calculate the total work**: The total amount of work done can be represented in terms of man-days. If 6 men can complete the job in 14 days, the total work is:
Total Work = 6 men × 14 days = 84 man-days
2. **Determine the new time frame**: Now, if we allow 21 days to complete this same job, we need to find out how many men would be required to finish it in that time.
3. **Calculate the required number of men**: To find out the number of men needed to complete the same amount of work in 21 days, we set up the equation:
Number of men × 21 days = 84 man-days
4. **Rearrange the equation** to solve for the number of men:
Number of men = 84 man-days / 21 days
5. **Calculate**:
Number of men = 4 men
6. **Compare the number of men**: Finally, we compare the number of men required now (4 men) to the original number of men (6 men). To find out how many fewer men are needed:
Fewer men = Original men – Required men = 6 men – 4 men = 2 men
So, if the men are allowed 21 days for the job, 2 fewer men would be needed.