In an 800 m race, A can beat B by 40 m (so B covers 760 m when A finishes 800 m). In a 500 m race, B can beat C by 5 m (so C covers 495 m when B finishes 500 m). By how much does A beat C in a 200 m race?

Introduction / Context:
Racing comparison problems are solved by converting finish advantages into speed ratios, then chaining those ratios. Once the overall speed ratio between two athletes is known, scale it to any race length to compute finish separations.

Given Data / Assumptions:

• A vs B (800 m): vA/vB = 800/760 = 20/19.
• B vs C (500 m): vB/vC = 500/495 = 100/99.
• We need A vs C over 200 m.

Concept / Approach:
Multiply ratios: vA/vC = (vA/vB) * (vB/vC) = (20/19) * (100/99) = 2000/1881. When A runs 200 m, C runs 200 / (vA/vC). The difference gives the margin by which A beats C.

Step-by-Step Solution:

Verification / Alternative check:
Using proportional times gives the same outcome because distance at equal time is proportional to speed.

Why Other Options Are Wrong:
12.7 m and the centimeter-scaled distractors are not consistent with the compounded ratio 2000/1881.

Common Pitfalls:
Adding raw meter advantages directly across different race lengths; advantages must be translated to speed ratios first.

Final Answer:
11.9 m