Transferring race results between contestants: In a 1 km race, A beats B by 100 m and C by 200 m. By how many metres can B beat C in a 1350 m race?

Introduction / Context:
We derive B:C speed ratio from A’s known advantages over B and C, then project that ratio to a new race distance to find B’s margin over C.

Given Data / Assumptions:

• A beats B by 100 m → when A runs 1000 m, B runs 900 m → vA/vB = 10/9.
• A beats C by 200 m → vA/vC = 1000/800 = 5/4.
• Uniform speeds.

Concept / Approach:
vB/vC = (vA/vC)/(vA/vB) = (5/4)/(10/9) = 9/8. In a 1350 m race for B, C covers 1350 * (8/9). Margin = difference.

Step-by-Step Solution:

Verification / Alternative check:
Scaling to any distance preserves the 9:8 proportion; 150 m follows directly.

Why Other Options Are Wrong:
120/210 m are off the proportion; 1200 m is a misread of C’s distance, not the margin.

Common Pitfalls:
Confusing margin with distance covered by the slower runner.

Final Answer:
150 m