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?

Question

Solve this multiple-choice question and choose the correct option.

Curioustab · Accepted Answer

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: A:C = (4/3)*(25/24) = 100/72 = 25/18If A runs 200, C runs 200*(18/25) = 144Lead = 200 − 144 = 56 m 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

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?

Answer

Explanation