A, B, and C can finish a work in 16, 32, and 48 days, respectively. They all start together. A works until completion; C leaves 2 days before the work is finished; B leaves 1 day before completion. In how many days is the work completed?

Introduction / Context:
This problem requires piecewise accounting of contributions because the team composition changes over the last two days. Add work across three intervals with correct rates and durations, then solve for the total time T.

Given Data / Assumptions:

• A = 1/16 per day (works throughout T days).
• B = 1/32 per day (works up to T - 1 days).
• C = 1/48 per day (works up to T - 2 days).

Concept / Approach:
Split the timeline: [0, T-2): A+B+C; [T-2, T-1): A+B; [T-1, T): A only. Sum contributions and set equal to 1 job, then solve for T.

Step-by-Step Solution:

Verification / Alternative check:
Approximate check: A alone would take 16 days; team support early on reduces time to a bit under 10 days, consistent with 9.36 days.

Why Other Options Are Wrong:
Integer guesses (10, 15, 20, 30) ignore the piecewise nature; only 9 4/11 satisfies the exact partitioned-rate equation.

Common Pitfalls:
Assuming constant team composition or forgetting to split the last two days correctly.

Final Answer:
9 4/11 days