If 5 spiders can catch five flies in five minutes, how many flies can hundred spiders catch in 100 minutes?

### Concept & Proportional Work This is a classic variation of the chain rule. The number of flies caught is the "work" done. The effort is the number of spiders multiplied by the time they spend catching. $$ \frac{M_1 D_1}{W_1} = \frac{M_2 D_2}{W_2} $$ ### Step-by-Step Solution * Identify scenario 1 variables: $M_1 = 5 \text{ spiders}$, $D_1 = 5 \text{ minutes}$, $W_1 = 5 \text{ flies}$. * Identify scenario 2 variables: $M_2 = 100 \text{ spiders}$, $D_2 = 100 \text{ minutes}$, $W_2 = x \text{ flies}$. * Plug the values into the formula: $$ \frac{5 \times 5}{5} = \frac{100 \times 100}{x} $$ * Simplify the left side of the equation: $\frac{25}{5} = 5$. * The equation is now: $5 = \frac{10000}{x}$. * Solve for $x$ by rearranging: $x = \frac{10000}{5}$. * Calculate the final value: $x = 2000$. ### Exam Strategy & Shortcut Understand the logical baseline: If 5 spiders catch 5 flies in 5 minutes, it means 1 spider catches 1 fly in 5 minutes. (Their rate is 1 fly per 5 minutes per spider). Therefore, in 100 minutes, 1 spider would catch $100 \div 5 = 20$ flies. Since there are 100 spiders, they will catch $100 \times 20 = 2000$ flies. ### Common Pitfall The most common psychological trap is the "parallel numbers" illusion. Because it's 5 spiders, 5 flies, 5 minutes, the brain naturally assumes 100 spiders, 100 minutes means 100 flies. Always rely on the mathematical formula rather than intuition here. ### Final Answer Therefore, the correct answer is **2000**.