Building vs. breaking: net progress with an interrupter A can build a structure in 8 days, while B can demolish the same structure in 3 days. A works alone for 4 days, then B joins and they work together for 2 days. After that, in how many days will.

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

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Introduction / Context:This problem involves a positive builder and a negative (demolisher) worker. When they work together, the net effect can reduce prior progress, so careful fraction accounting is essential. Given Data / Assumptions: A builds in 8 days ⇒ +1/8 per day. B breaks in 3 days ⇒ −1/3 per day. A works 4 days alone; then A and B work together for 2 days; finally A works alone again. Concept / Approach:Track cumulative progress: first A alone, then the net effect with B, then compute the remaining fraction for A alone. Step-by-Step Solution: After first 4 days (A alone): 4 * (1/8) = 1/2 builtA + B per day: 1/8 − 1/3 = (3 − 8)/24 = −5/24Two days together: 2 * (−5/24) = −5/12Progress after 6 days: 1/2 − 5/12 = 1/12 builtRemaining = 1 − 1/12 = 11/12Time for A alone = (11/12) / (1/8) = 88/12 = 22/3 days Verification / Alternative check:Multiply A’s rate by 22/3 to confirm: (1/8)*(22/3) = 22/24 = 11/12, exactly the remainder. Why Other Options Are Wrong:7, 8, 9 days are integer guesses; only 22/3 satisfies the exact net accounting. Common Pitfalls:Ignoring the negative contribution when B is demolishing or forgetting that net can decrease progress. Final Answer:22/3 days

Building vs. breaking: net progress with an interrupter A can build a structure in 8 days, while B can demolish the same structure in 3 days. A works alone for 4 days, then B joins and they work together for 2 days. After that, in how many days will A alone build the remaining structure?

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