The Persistent snail

Question

A snail lives in a 20-foot well, at dawn, he began to climb to the top of the well at the rate of 3 inches per hour for each of the twelve daylight hours. Each night he slipped back at the rate of 2 inches per hour. How long did it take the snail to escape?

Answer 1

20 feet= 20(12) inches = 240 inches

3 inches- 2 inches per hour for 12 hours = 12 inches per day

240/12 = 20 days to reach the top

but that's slightly too long. there's a little nuance to the problem. Once the snail reaches the time in the day time, it won't slip back that following night.

after 19 1/2 24 hour days, the snail went 20x12x3 = 720 inches up and 19x12x2 = 456 inches down for a net

720-456 = 264 inches > 240 inches.

264-240 = 24 inches reached in 24/3 = 8 hours

19 1/2 24 hour days minus 8 hours

= 19.5(24)- 8

= 468-8

= 460 hours to reach the top

=460/24 = 19 1/6 days

20 days is almost more than 1 day more than needed

after 19 days & nights, the snail has reached 12x19 = 228 inches, 20 feet = 240 inches. in another 12/3 of daylight = 4 hours it will reach the top. 19 days and 4 hours = 19 4/24 = 19 1/6 total days to reach the top.