If 7 spiders make 7 webs in 7 days, in how many days will 1 spider make 1 web, assuming all spiders work at the same constant rate?

Introduction / Context:
This interesting time and work problem is framed with spiders and webs instead of men and work. The underlying concept is exactly the same: total work is proportional to the number of workers and the time they spend working. Here, we need to interpret the given information correctly to find the time needed for a single spider to produce a single web.

Given Data / Assumptions:

• Seven spiders make seven webs in seven days.
• All spiders work at the same constant rate and independently.
• The nature of each web is identical so that the work per web is the same.
• We must find how many days one spider will take to make one web.

Concept / Approach:
First, we determine the rate at which webs are produced per spider per day. The information that seven spiders make seven webs in seven days tells us the total output of the group over that period. Using this, we can derive the work rate of one spider and then compute the time required for one spider to complete one web. This is essentially a unitary method problem.

Step-by-Step Solution:
Step 1: Find the total number of spider days in the given situation. Seven spiders working for seven days produce 7 * 7 = 49 spider days of work.Step 2: The total number of webs produced in that time is given as 7.Step 3: Therefore, the production rate is 7 webs per 49 spider days, which simplifies to 1 web per 7 spider days.Step 4: One spider day is defined as one spider working for one day. Thus, one spider taking 7 spider days means that the same spider works for 7 days to produce one web.Step 5: Hence, one spider will complete one web in 7 days.
Verification / Alternative check:
We can interpret the original statement in another way. If each spider produces webs independently at the same rate, then in seven days each spider must have produced exactly one web for the total of seven webs to be achieved by seven spiders. Therefore, by simple reasoning, one spider in seven days produces one web, which is consistent with the unitary method result. This double check reinforces the conclusion.

Why Other Options Are Wrong:
One day would suggest that one spider can produce one web in one day. That would mean seven spiders in seven days would produce 49 webs, which contradicts the given information.Three days would imply a higher individual production rate than is supported by the data. Multiplying back would not yield seven webs in seven days for seven spiders.Fourteen days would imply that a spider works more slowly than indicated by the given scenario, because the group output would be too small if each web took 14 days for one spider.
Common Pitfalls:
Many students misread the problem and think it describes a situation where 7 spiders together build a single web in 7 days. In fact, the wording clearly states that seven spiders build seven webs. Another source of confusion is mixing up spider days and human intuition about how quickly a spider spins a web. Focusing only on the numerical relationships in the problem avoids these distractions.

Final Answer:
One spider will make one web in 7 days.