Climbing monkey — climbs 30 ft at the start of each hour and then slips back 20 ft while resting. Starting at 8:00 a.m., when does it first reach a flag at 120 ft?

Introduction / Context:
This is a stepwise-motion puzzle with progress and slippage in discrete hourly cycles. The key is to track the height after each hour, remembering that upon reaching or exceeding the target during the climb, the monkey succeeds before any slip occurs.

Given Data / Assumptions:

• Each hour starts with a 30 ft climb, followed by a rest during which it slips 20 ft.
• Net gain per full hour (climb + slip) = 10 ft.
• Target height = 120 ft; start time = 8:00 a.m.

Concept / Approach:
Compute the height at the end of each hour including slippage. However, in the final successful hour, the flag is reached during the climb, before any slip. Therefore, stop counting as soon as the climbing phase hits 120 ft.

Step-by-Step Solution:

Verification / Alternative check:
General shortcut: find the last pre-climb base height from which +30 reaches or exceeds 120. That base is 90 ft; the schedule shows the base of 90 ft occurs at 5 p.m., so success is achieved during that hour’s initial climb.

Why Other Options Are Wrong:

• 4 p.m. — base only 80 ft; cannot reach 120 in that hour’s climb.
• 6 p.m. — too late; already reached at the start of the 10th hour.
• None of these — invalid because 5 p.m. is correct.

Common Pitfalls:
Multiplying net gain by hours without accounting for the final hour’s “no slip after reaching target.” Always separate the last partial hour from the full cycles.

Final Answer:
5 p.m.