Workers A and B can complete a job individually in 8 hours and 12 hours, respectively. If they work in alternate one-hour turns, starting with A, at what time (duration) will the job be completed?

Introduction / Context:
Alternate-work problems require tracking the cumulative fraction completed after each segment. With 1-hour alternations, we can bundle two successive hours (one by A, one by B) into a 2-hour cycle to simplify computation.

Given Data / Assumptions:

• A's solo time = 8 h ⇒ rate = 1/8 per hour.
• B's solo time = 12 h ⇒ rate = 1/12 per hour.
• Work proceeds in 1-hour blocks with A starting.

Concept / Approach:
In each 2-hour cycle (A then B), the completed fraction equals 1/8 + 1/12. Repeatedly add cycle output until the remaining fraction can be finished by a partial final hour if needed.

Step-by-Step Solution:

Verification / Alternative check:
Breaking into hour-by-hour sums yields the same cumulative fraction; cycle grouping just accelerates calculation.

Why Other Options Are Wrong:
9 h: stops too early (1/24 remains). 8 1/2 h and 8 h: underestimate combined progress. 10 h: overshoots by an extra half-hour.

Common Pitfalls:
Forgetting partial hours are allowed; mis-adding fractions in cycles; assuming a whole-hour completion.

Final Answer:
9 1/2 h