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

Introduction / Context:
This is a simple but slightly tricky work and rate puzzle involving spiders and webs. It is designed to see if you understand the concept of uniform work rates and how to convert a group's total work over time into an individual rate. The numbers are deliberately all sevens to tempt quick but careless answers, so careful reasoning is important.

Given Data / Assumptions:

• 7 spiders make 7 webs in 7 days.
• All spiders are assumed to work at the same constant rate.
• Each web is considered to require the same amount of work.
• We are asked for the time taken by 1 spider to make 1 web.

Concept / Approach:
We treat "web" as the unit of work. The key idea is to find the overall work rate of the group (spiders per day per web) and then divide by the number of spiders to find the rate per spider. Once we know the daily rate of a single spider, we can compute the time required for that spider to produce one web. This is exactly analogous to workers completing units of work.

Step-by-Step Solution:
Step 1: Total work is 7 webs. Step 2: Total time for 7 spiders together to make 7 webs is 7 days. Step 3: Combined rate of 7 spiders = total webs / total days = 7 webs / 7 days = 1 web per day. Step 4: This 1 web per day is produced by 7 spiders working together. Step 5: Therefore, rate of 1 spider = (1 web per day) / 7 = 1/7 web per day. Step 6: Time required for 1 spider to make 1 web = 1 web / (1/7 web per day) = 7 days.

Verification / Alternative check:
We can also reason directly: if 7 spiders make 7 webs in 7 days, then each day the group creates 1 web. It takes 7 spiders to create that 1 web in a day. To get 1 web from just a single spider, you need 7 times as long, since the workforce is 7 times smaller. That leads to 7 days, which matches our rate-based calculation.

Why Other Options Are Wrong:
1 day is wrong because that would imply 1 spider makes 1 web per day, so 7 spiders would make 7 webs per day, meaning 7 webs would be completed in just 1 day, not 7. 3.5 days would mean the group could produce more than 7 webs in 7 days, which contradicts the original statement. 14 and 49 days are both far too large; they would make the combined rate inconsistent with the given data.

Common Pitfalls:
A typical error is to assume that because the numbers are all sevens, 1 spider should take 1 day, without considering the work rate distribution. Another pitfall is mixing up who is doing the work (the whole group versus one individual). Always translate the word problem into total work, group rate, individual rate, and then time, in that order.

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