What if a caterpillar is climbing out of a glass that is 12 inches high

Question

What if a caterpillar is climbing out of a glass that is 12 inches high and can climb 1 (1/2) inches in an hour but slides and falls back (1/4) during the hour it rests. How long will it take the caterpillar to climb to the top of the jar?

Answer 1

Hi Tim. If the caterpillar climbs 1/2 inches in 1 hour, and falls back 1/4 inches in the hour it rests, then after 2 hours it only nets 1/4 inches. (1/2 - 1/4 = 1/4). To reach 12 inches at the top of the glass, it will take 8 hours for 1 inch (since it’s 2 hours for 1/4 inch), and then 96 hours for 12 inches. (12 x 8 = 96).

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Answer 2

the caterpillar travels 1.25 in every two hours.

In nine trips the caterpillar travels 9(1.25) or 11.25 in

9 trips take 18 hours.

In the 19th hour the caterpillar climbs out or the glass to freedom, Yah!