1st hour: up 3 ft. + (–2 ft. backwards) = 1 ft.
On the first try, you climb 1 foot.
2nd hour: 1 ft. + up 3 ft. + (–2 ft. backwards) = 2 ft.
On the second try, you begin at 1 foot and gain one additional foot.
3rd hour: 2 ft. + up 3 ft. + (–2 ft. backwards) = 3 ft.
On the third try, you start at 2 feet and gain one additional foot.
4th hour: 3 ft. + up 3 ft. + (–2 ft. backwards) = 4 ft.
And so on . . .
16th hour: 15 ft. + up 3 ft. = 18 ft. Answer: It will take you 16 hours to climb out of the hole. On the 16th try you will begin at 15 feet, and as you climb up three more feet you will reach 18 feet. You should be able to climb out before you slide back two feet!
