If 10 spiders can catch 10 flies in 10 minutes (all working at the same constant rate), how many flies can 200 spiders catch in 200 minutes?

Introduction: Catching flies here scales with the number of spiders and with time, assuming a constant per-spider catch rate. We infer the rate from the base scenario and then scale to the larger numbers using direct proportionality (spiders × minutes × rate per spider-minute).

Given Data / Assumptions:

• 10 spiders catch 10 flies in 10 minutes.
• All spiders have the same constant efficiency.
• Find flies caught by 200 spiders in 200 minutes.

Concept / Approach: Let r be the number of flies caught by one spider per minute. Then total flies = spiders × minutes × r. Using the base case we find r, then apply it to the new case by multiplication without rounding since values are exact here.

Step-by-Step Solution:

Verification / Alternative check: Proportion method: New/Base = (200/10) * (200/10) = 20 * 20 = 400. Then 10 * 400 = 4000, same result.

Why Other Options Are Wrong: 2000, 3000, 5000, 2500 are not consistent with the direct quadratic scaling in spiders and minutes based on the stated rate.

Common Pitfalls: Treating the relationship as linear in one factor only (either spiders or minutes). The catch count scales with both.

Final Answer: 4000