A snail sits at the bottom of a 30-foot wall. Each hour it can climb three feet, but it then slips down two feet. How long does it take the snail to reach the top?
Question
A snail sits at the bottom of a 30-foot wall. Each hour it can climb three feet, but it then slips down two feet. How long does it take the snail to reach the top?
Solution
Sure, let's break this problem down:
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In one hour, the snail effectively climbs 1 foot. This is because it climbs 3 feet and then slips down 2 feet (3 feet - 2 feet = 1 foot).
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However, once the snail reaches the top, it won't slip down anymore. So, for the last climb, it will climb 3 feet without slipping down.
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Therefore, we need to consider the wall as being 2 feet shorter, or 28 feet, because for the last climb the snail will climb 3 feet without slipping.
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At a rate of 1 foot per hour, it will take the snail 28 hours to climb 28 feet.
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Then, it will take an additional 1 hour to climb the last 3 feet.
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So in total, it will take the snail 29 hours to reach the top of the 30-foot wall.
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