Transitive race advantage: In a 200 m race, A beats B by 50 m and B beats C by 8 m. By how much does A beat C in 200 m?

Introduction / Context:Infer speed ratios from two pairwise results and combine to compare A and C directly.

Given Data / Assumptions:

• A:B in 200 m ⇒ 200:150 = 4:3
• B:C in 200 m ⇒ 200:192 = 25:24

Concept / Approach:Multiply ratios for A:C, then scale to 200 m to find C’s distance at A’s finish.

Step-by-Step Solution:

Verification / Alternative check:Cross-check by finding C’s speed as a fraction of A’s from chained ratios.

Why Other Options Are Wrong:They don’t reflect the chained ratio 25:18 scaled to 200 m.

Common Pitfalls:Subtracting the leads (50 and 8) instead of combining ratios.

Final Answer:56 m