Linked race comparisons: In a 600 m race A beats B by 30 m; in a 500 m race B beats C by 25 m. By how many metres will A beat C in a 400 m race?

Introduction / Context:
We infer speed ratios from separate races and combine them to compare A and C in a new race length.

Given Data / Assumptions:

• A vs B in 600 m: A:B = 600:570 = 20:19
• B vs C in 500 m: B:C = 500:475 = 20:19
• Target race length for A = 400 m

Concept / Approach:
Multiply ratios to get A:C and then scale to 400 m to find C’s distance at A’s finish.

Step-by-Step Solution:

Verification / Alternative check:
Ratios reduce consistently; no units needed as they cancel in ratios.

Why Other Options Are Wrong:
Other leads mismatch the squared ratio 400:361 implied by chaining 20:19 twice.

Common Pitfalls:
Adding distance leads directly; proper method is via speeds/ratios.

Final Answer:
39 m