Final answer:
To determine how long it will take 6 men to dig the well that 5 men can dig in 20 days, we use the concept of man-days, resulting in approximately 16.67 days for 6 men to complete the work.
Step-by-step explanation:
If five men can dig a well for 20 days, we can calculate the total man-days of work done, which is the number of men multiplied by the number of days they work.
In this case, 5 men * 20 days = 100 man-days.
This is the total amount of work needed to dig the well.
If six men are set to complete the same amount of work (100 man-days), we divide the total man-days by the number of men to find out how many days it would take for 6 men to complete the work.
Hence, 100 man-days / 6 men = approximately 16.67 days.
Therefore, it will take 6 men around 16.67 days to dig the same well.