Question

There is an old riddle about a frog at the bottom of a 20-foot well. if he climbs up 3 feet each day and slips back 2 feet each night, how many days will it take him to reach the 20-foot mark and climb out of the well?

Answer 1

For this case what we are going to do is write step by step the equation of the line
f (x) = mx + b
We have:
20-foot well:
f (x) = mx + 20
if he climbs up 3 feet each day and slips back 2 feet each night:
f (x) = - 3x + 2x + 20
f (x) = - x + 20
When it reaches 20 feet we have f (x) = 0:
f (x) = - x + 20
0 = -x + 20
x = 20 days.
Answer:
It will take him 20 days to reach the 20-foot mark and climb out of the well