A can beat B by 5 m in a 100 m race (so B covers 95 m when A covers 100 m). B can beat C by 15 m in a 200 m race (so C covers 185 m when B covers 200 m). By how many meters will A beat C in a 400 m race?

Introduction / Context:Convert finish advantages to speed ratios and chain them to compare two runners who have not raced directly. Once vA/vC is obtained, scale to the target race to compute the margin.

Given Data / Assumptions:

• vA/vB = 100/95 = 20/19.
• vB/vC = 200/185 = 40/37.
• Target race length for A = 400 m.

Concept / Approach:vA/vC = (20/19)*(40/37) = 800/703. When A runs 400 m, C runs 400 / (800/703) = 703/2 = 351.5 m, giving the margin.

Step-by-Step Solution:

Verification / Alternative check:Time ratio cross-check gives the same margin because distance at equal time ∝ speed.

Why Other Options Are Wrong:50.5, 45.5, 42.5 m do not align with the compounded ratio.

Common Pitfalls:Adding meter advantages directly rather than converting to speed ratios first.

Final Answer:48.5 m