Question

A frog is climbing out of a well that is 31 feet deep. The frog can climb 3 feet per hour but then it rests for an hour, during which it slips back 2 feet. How long will it take for the frog to get out of the well?

What if the well was 74 feet deep, the frog climbs 7 feet per hour, and it slips back 2 feet while resting? (Round your answer to the nearaest hour.)


(c) What if a caterpillar is climbing out of a glass that is 11 inches high and can climb 1 and 1/2 inches in an hour but slides and falls back 1/4th inch during the hour it rests. How long will it take the caterpillar to climb to the top of the jar? (Round your answer to the nearest hour.)

Answer 1

The height of the wall = 31 feet.

Frog climbs 3 feet per hour and then falls back 2 feet in next hour as it is taking rest.

So, on an average for two hours, it climbs 1 step.

So, for climbing 28 steps, it requires on an average 2 hours for every step.

28X2 = 56 hours in total.

The remaining 3 steps, it climbs in the first hour itself and it is not needed to take the rest again for these last three steps. So, 56 hours of 28 steps and then 1 hour for 3 steps at a time.

total of 57 hours for climbing 31 steps

b) height of well = 74 feet

frog climbing rate = 7 steps per hour and slips back 2 feet while resting for an hour.

So, on an average it climbs 5 steps for 2 hours except the last few steps.

So, out of the 74 steps, 70 steps it can climb at a rate of 5 steps per 2 hours.

i.e 70/5 X 2 = 28 hours. For the last 4 steps, it climbs in 4/7 th of the hour.

i.e total of 28.57 hours.

implies it takes total of 29 hours for 74 steps.

c)

Height of grass = 11 inches

Caterpillar average climbing rate for 2 hours

= 1.5 inches climbing - 0.25 inches fall

= 1.25 inches per 2 hours.

For first 10 inches it takes, 10/1.25 X 2 = 16 hours.

Afther that, the remaining 1 inch it can climb within an hour without taking any rest.

So, it can climb the remaining inch in 1/1.5 = 0.67 hours

SO, total of 16.67 hours

= rounding it , total 17 hours required for caterpillar to climb the grass of 11 inches.