Four mat weavers can weave four mats in four days. At the same rate of working, how many mats will be woven by eight mat weavers in eight days?

Introduction / Context:
This is a classic direct proportion and work rate problem. It relates the number of workers, the time they work and the amount of work done. Here, mat weavers produce mats, and we are asked to scale up the situation when both the number of workers and the number of days are doubled.

Given Data / Assumptions:

• 4 mat weavers weave 4 mats in 4 days.
• All weavers work at the same constant rate.
• The new situation involves 8 mat weavers working for 8 days.
• We must find how many mats they will produce.

Concept / Approach:
First, determine the rate of mat production per weaver per day. Then multiply that rate by the total number of weaver days in the new situation. This is a straightforward chain rule problem where work is proportional to workers multiplied by time.

Step-by-Step Solution:
Step 1: Total weaver days in the original case = 4 weavers * 4 days = 16 weaver days.Step 2: These 16 weaver days produce 4 mats.Step 3: So production rate = 4 mats / 16 weaver days = 0.25 mat per weaver day.Step 4: In the new case, we have 8 weavers working for 8 days, so number of weaver days = 8 * 8 = 64.Step 5: Total mats produced = 64 * 0.25 = 16 mats.

Verification / Alternative check:
Notice that we doubled both the number of weavers and the number of days compared with the original setup. Doubling weavers and doubling time multiplies the total work by 4. Originally 4 mats were woven, so in the new setup they should weave 4 * 4 = 16 mats. This quick proportional check matches the detailed calculation.

Why Other Options Are Wrong:
4 mats corresponds to the original arrangement, not the increased one. 8 and 12 mats underestimate the effect of doubling both workers and days. 20 mats would require a higher rate than what is given by the original information.

Common Pitfalls:

• Forgetting to multiply both the number of weavers and the number of days when computing weaver days.
• Assuming that doubling workers doubles mats, but overlooking that days also doubled, which gives a factor of 4.
• Misinterpreting the phrase four weavers weave four mats in four days as one weaver per mat without verifying the rate.

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