A well is 18 feet deep. A snail at the bottom climbs up 4 feet each day and slips back 2 feet each night. How many days will it take the snail to reach the top of the well? Answer the questions in parts a, b, c,
and d.
a. What is the greatest height the snail reaches during the first 24 hours? 4 feet
How far up the well will the snail be at the end of the first 24 hours? 2 feet
b. One plan that is commonly chosen is to compute 18/2, since it appears that the snail gains 2 feet each
day. However, 9 days is not the correct answer. A second plan is to make a drawing, as shown here, and
to plot the snail's daily progress. What is the snail's greatest height during the second day? 4 feet
18
0.
c. Trace out the snail's daily progress, and mark its position at the end of each day. How many days
does it take the snail to get out of the well? 8 days
d. There is a "surprise ending" at the top of the well because the snail does not slip back on the last day.
Suppose a well is 27 feet deep and the snail climbs up 6 feet each day and slips back 3 feet each night,
how many days will it take the snail to reach the top of the well?
days