Four mat-weavers can weave four mats in four days. Working at the same constant rate, how many mats would be woven by eight mat-weavers in eight days?

Introduction / Context:
This question is another work-rate problem, but framed in terms of mat-weavers and mats. It checks your understanding of direct proportion between the number of workers, the time they work, and the number of items produced, assuming a constant rate of production per worker.

Given Data / Assumptions:
- 4 mat-weavers weave 4 mats in 4 days.
- All weavers have the same constant weaving rate.
- We need the number of mats woven by 8 mat-weavers in 8 days.

Concept / Approach:
We can express total work in weaver-days and mats. First, we compute how many mats are produced per weaver-day. Then we multiply this rate by the total weaver-days in the new scenario (8 weavers for 8 days) to find the total mats produced.

Step-by-Step Solution:
Step 1: Compute total weaver-days in the initial situation: 4 weavers * 4 days = 16 weaver-days.Step 2: Total mats produced = 4 mats.Step 3: Mats per weaver-day = 4 mats / 16 weaver-days = 1/4 mat per weaver-day.Step 4: In the new situation, we have 8 weavers working for 8 days.Step 5: Total weaver-days now = 8 * 8 = 64 weaver-days.Step 6: Total mats produced = 64 weaver-days * (1/4 mat per weaver-day) = 64 * 1/4 = 16 mats.

Verification / Alternative check:
Use simple chain rule: compare the second situation to the first. The number of weavers doubles (4 → 8), and the number of days also doubles (4 → 8). So the total work should increase by a factor of 2 * 2 = 4. Originally, 4 mats were made. 4 times that is 16 mats. This matches the weaver-day method.

Why Other Options Are Wrong:
8 mats would be correct if only one of the two factors (either weavers or days) doubled, but both increased. 12 or 24 mats do not match the precise factor of 4 increase and typically arise from partial reasoning or arithmetic errors. 4 mats would mean no increase in production despite more weavers and more time, which is clearly inconsistent.

Common Pitfalls:
Some learners forget to consider both changes (workers and days) or mix up whether the relationship is direct or inverse. Others miscalculate the factor of increase. Always think in terms of total worker-days and then scale production accordingly.

Final Answer:
Eight mat-weavers will weave 16 mats in eight days.