If 9 spiders make 9 webs in 9 days, then 13 spiders will make 13 webs in how many days?

1. Break Down the Problem

We need to determine the number of days required for 13 spiders to make 13 webs, given that 9 spiders make 9 webs in 9 days.

2. Relevant Concepts

From the problem, we can deduce the relationship between the number of spiders, the number of webs, and the number of days. If 9 spiders can produce 9 webs in 9 days, then 1 spider produces 1 web in 9 days.

3. Analysis and Detail

• From the initial condition: $\text{Rate of 1 spider} = \frac{1 \text{ web}}{9 \text{ days}}$

• Now, for 13 spiders working at the same rate: $\text{Rate of 13 spiders} = 13 \times \frac{1 \text{ web}}{9 \text{ days}} = \frac{13 \text{ webs}}{9 \text{ days}}$

4. Verify and Summarize

Both the number of webs (13) and the rate of production stay proportional. Therefore, 13 spiders will still take the same time to produce 13 webs as 9 spiders take to produce 9 webs, which is 9 days.

Final Answer

Thus, 13 spiders will make 13 webs in 9 days.