A team of 48 people can complete a certain task in 17 days. After they have worked together for 6 days, 4 workers leave the team. Starting from that moment, in how many additional days will the remaining workers take to complete the remaining work?

Introduction / Context:
This is a straightforward work and manpower distribution problem. We are told how long a team of 48 people takes to complete a task, and then some workers leave before the work is finished. The objective is to calculate how much additional time the reduced team needs to complete the remaining part of the work. This question tests your understanding of total work, work already done, and the work rate of the remaining team.

Given Data / Assumptions:

• 48 people complete the task in 17 days.
• They work together for 6 days initially.
• After 6 days, 4 people leave, leaving 44 people.
• We assume constant efficiency for each worker and that work is distributed uniformly.
• Total work is taken as 1 unit.

Concept / Approach:
We first compute the total work in terms of man-days, that is, number of workers multiplied by days. We then calculate how much of this work is completed in the first 6 days by the initial team. The remaining work can then be calculated. With fewer workers, we compute the new daily work rate and finally determine the number of additional days needed to finish the remaining work.

Step-by-Step Solution:
Step 1: Compute total work in man-days. Total work = 48 workers * 17 days = 816 man-days. Step 2: Work done in the first 6 days by 48 workers = 48 * 6 = 288 man-days. Step 3: Remaining work in man-days = total man-days - work already done = 816 - 288 = 528 man-days. Step 4: After 6 days, 4 workers leave. Remaining workers = 48 - 4 = 44. Step 5: Let the number of additional days required be D. Then work done by 44 workers in D days = 44 * D man-days. Step 6: This must equal the remaining work of 528 man-days, so 44 * D = 528. Step 7: Solve for D: D = 528 / 44 = 12 days.

Verification / Alternative check:
We can quickly verify by checking total time. First 6 days with 48 workers plus 12 more days with 44 workers completes the task. It is consistent with the total of 816 man-days, so the answer is coherent. Additionally, as the number of workers has only slightly decreased, the extra time compared with the original 17 days is not very large, which aligns with our result.

Why Other Options Are Wrong:

• 13 days: This would give 44 * 13 = 572 man-days, which exceeds the remaining work requirement.
• 15 days: 44 * 15 = 660 man-days, which is far more than needed and does not fit the total work calculation.
• 16 days: 44 * 16 = 704 man-days, which again is too large and inconsistent with the total work of 816 man-days.

Common Pitfalls:
Learners may forget to think in terms of total man-days and may attempt to directly manipulate the days without accounting for the changing team size. Another common error is subtracting days instead of calculating the remaining work explicitly. Also, mixing up the order and incorrectly using 17 - 6 instead of working with man-days can lead to incorrect results.

Final Answer:
From the moment 4 workers leave, the remaining team will need 12 days to finish the task.