Seven spiders can weave seven complete webs in seven days. Assuming all spiders work at the same constant rate, in how many days will one spider weave one web?

Introduction / Context:This question is a neat illustration of unitary method and work-rate reasoning. It appears simple at first glance but can be confusing if you only look at the numbers superficially. The key is to think in terms of total spider-days needed per web rather than trying to guess directly.

Given Data / Assumptions:- 7 spiders weave 7 webs in 7 days.- All spiders are equally efficient and work continuously at the same rate.- We want the time required for 1 spider to weave 1 web.

Concept / Approach:The best way to handle this is to calculate the total work and express it in spider-days. Then you can find how many spider-days are required to make a single web. Finally, you translate spider-days into days for one spider. Total work is measured in “webs”, while effort is measured in “spider-days”.

Step-by-Step Solution:Step 1: Compute total spider-days used in the given situation: 7 spiders * 7 days = 49 spider-days.Step 2: The result of this effort is 7 webs. So, 7 webs require 49 spider-days.Step 3: Therefore, 1 web requires 49 / 7 = 7 spider-days.Step 4: If 1 spider is working alone, each day contributes exactly 1 spider-day.Step 5: To accumulate 7 spider-days, one spider will need 7 days.Step 6: Hence, one spider will weave one web in 7 days.

Verification / Alternative check:You can also reason proportionally: the situation “7 spiders make 7 webs in 7 days” is symmetric. Intuitively, that means each spider effectively makes 1 web in 7 days, since there are 7 spiders and 7 webs. This matches the more formal spider-day calculation.

Why Other Options Are Wrong:1 day and 3 days are too short and would imply each spider makes multiple webs in 7 days, contradicting the original data. 14 or 21 days are too long and would give fewer than 7 webs in 7 days if all spiders were working at those speeds. Only 7 days is consistent with the total of 7 webs from 7 spiders in 7 days.

Common Pitfalls:Some learners misinterpret the statement and think “7 spiders, 7 webs, 7 days” automatically means 1 day for 1 web, forgetting that the work is shared. Others mix up proportionality, assuming work per spider per day is 1 web, which clearly contradicts the total. Using spider-days as a unit of effort helps avoid these errors.

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