Chaining two race advantages: In a 600 m race, A beats B by 60 m. In a 500 m race, B beats C by 50 m. By how many metres will A beat C in a 400 m race?

Introduction / Context:
When advantages are given for different race lengths, convert each advantage to a speed ratio, multiply the ratios to compare non-adjacent contestants, and then scale to the desired length.

Given Data / Assumptions:

• A vs B at 600 m: B at 540 m when A finishes → vA/vB = 600/540 = 10/9.
• B vs C at 500 m: C at 450 m when B finishes → vB/vC = 500/450 = 10/9.
• Uniform speeds.

Concept / Approach:
Combine: vA/vC = (10/9)*(10/9) = 100/81. For 400 m, compute the distance C covers when A finishes.

Step-by-Step Solution:

Verification / Alternative check:
Repeating the derivation numerically yields the same 76 m difference for any proportional scaling.

Why Other Options Are Wrong:
78/56/86 are off the exact 100/81 ratio result.

Common Pitfalls:
Adding raw metre advantages; only ratios transfer correctly across distances.

Final Answer:
76 m