A medium question on climbing out of a well for P3, with a step-by-step solution, diagrams and the answer. Rarely set directly in competition papers, but a classic for learning to think about the last step on its own. Good for the younger years.
The question
A caterpillar climbs a bamboo pole 21 cm tall, starting at the bottom.
It climbs for 1 minute, going up 6 cm, then rests for 1 minute, sliding down 1 cm while it rests.
Then it climbs for a minute and rests for a minute again, over and over, always climbing at the same speed.
From leaving the bottom to reaching the top, how many minutes does the caterpillar take?
Show the hints (2)
💡Hint 1: One minute climbing plus one resting: in those 2 minutes, how much higher does it get?
💡Hint 2: After the climb that reaches the top there is no rest. Where must it be just before that last climb?
Worked solution
Have a go first, then read the solution step by step.
1.The last climb is 6 cm, so before it the caterpillar must be at 21 − 6 = 15 cm.
2.Each climb-and-rest gains 6 − 1 = 5 cm.
3.To get to 15 cm: 15 ÷ 5 = 3 rounds of climb-and-rest.
4.Time: 3 × 2 + 1 = 7 minutes (the last climb has no rest after it).
⚠️Common mistake: 4 × 2 = 8 minutes, counting a rest after the last climb.
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