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?

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Solve this multiple-choice question and choose the correct option.

Accepted Answer

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: Two-hour cycle output = 1/8 + 1/12 = 5/24 of the job.After 4 full cycles (8 hours), work done = 4 * (5/24) = 20/24 = 5/6; remaining = 1/6.Next hour A works: adds 1/8; remaining = 1/6 - 1/8 = 1/24.B's rate is 1/12 per hour, so time to finish the last 1/24 = (1/24) / (1/12) = 1/2 hour.Total duration = 8 h + 1 h + 0.5 h = 9.5 h = 9 1/2 h. 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

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?

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