Final answer:
It takes the snail 6 days to reach the top of a 16 m high well, as it makes an effective progress of 3 m per day and does not slip back on the final day.
Step-by-step explanation:
To determine how many days it took the snail to reach the top of a 16 m high well, considering it crawls 4 m up each day and slips back 1 m each night, we can calculate the effective progress per day and then find the total number of days required.
During the day, the snail makes a progress of 4 m, but at night it slips back 1 m, which results in an effective daily progress of 3 m. Since the snail is 1 m below the top by the evening of the last day, it does not slip back on the last night. Therefore, we need to account for 15 m (one meter less than the total height) to calculate the number of full days of progress.
So, we divide 15 m (effective height) by 3 m/day (effective progress per day) to get the number of full days it takes the snail to be 1 m from the top, which is 5 days. On the 6th day, the snail reaches the top without slipping back.
The answer is that it takes the snail 6 days to reach the top.