Algebra Level 3

One noon, an 8-centimeter caterpillar is trapped in a 1-meter deep hole. If:

  • Every other morning, the caterpillar grows half of its length
  • Every noon, the caterpillar travels up by 3/5 of its length
  • Every night, the caterpillar slips down 2/5 of its traveled distance

Given that the caterpillar starts travelling that same noon and it grows the next morning, how many days will it take for the caterpillar to get out of the hole?

Details and Assumptions

  1. The caterpillar grows downwards.

  2. Assume that when the caterpillar grows, the head is the fixed point. This means that the growth does not cause it to move higher.

(For example, if the caterpillar attains a distance of 8 cm by night and it grows half of its length the next morning, the caterpillar's head will be on the same spot but it will have its tail to represent the growth. The tail then will be moved downward.)


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