A monkey starts climbing up a tree 20ft.
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A monkey starts climbing up a tree 20ft. tall. Each hour, it hops 3ft. and slips back 2ft. How much time would it take the monkey to reach the top?
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Each hour the monkey gains 3 - 2 = 1 ft. At the end of 17 hours, it reaches 17 ft. In the 18th hour, it hops 3 ft and reaches 20 ft (the top) without slipping back.
Step-by-step Derivation:
Step 1: Net progress in 1 hour = 3 ft - 2 ft = 1 ft.
Step 2: On the final hop, the monkey covers 3 ft and reaches the top without slipping.
Step 3: Height before the last hop = 20 ft - 3 ft = 17 ft.
Step 4: Time to climb 17 ft at 1 ft/hr = 17 hours.
Step 5: In the 18th hour, it hops 3 ft to reach 17 + 3 = 20 ft. Total time = 18 hours.