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?

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:

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