how long will it take frog to climb out?

Question

A frog is climbing oht of a well that is 11 feet deep. The frog can climb 3 feet per hour but then it rests for an hour, during which it slips back one foot. How long will it take for the frog to get out of the well?

Answer 1

The frog starts from the bottom of the well.  We know that the well is 11 feet deep and that the frog can climb 3 feet per hour. Each time it climbs, it rests for an hour, and decreases its height by 1 foot. So if it reaches 3 feet in the first hour, then in the next hour it is 2 feet.  We continue this pattern until we get to 11 feet.

 

1st hour:     3

2nd hour:    3 - 1 = 2

3rd hour:     2 + 3 = 5

4th hour:     5 - 1 = 4

5th hour:     4 + 3 = 7

6th hour:     7 - 1 = 6

5th hour:     6 + 3 = 9

6th hour:     9 - 1 = 8

7th hour:     8 + 3 = 11

 

It takes the frog 7 hours to get out of the well.