In a 200 m race, A beats B by 31 m and C by 18 m. In a 350 m race, by how many metres will C beat B?

Problem restatement
From the 200 m results, infer the speed ratios and predict the B–C gap over 350 m.

Given data

• When A runs 200 m, B runs 169 m and C runs 182 m.
• Thus v_A : v_B = 200 : 169 and v_A : v_C = 200 : 182 = 100 : 91.

Concept/Approach
For the time B completes 350 m, C covers (v_C/v_B) × 350. Compute v_C/v_B from the two ratios.

Step-by-step calculation
v_C/v_B = (v_C/v_A) × (v_A/v_B) = (91/100) × (200/169) = 182/169 = 14/13 C's distance in B's 350 m time = (14/13) × 350 = 350 × 14 ÷ 13 = 376 12⁄13 m Winning margin (C over B) = 376 12⁄13 − 350 = 350 ÷ 13 ≈ 26.92 m

Verification/Alternative
Direct proportion: when B runs 169, C runs 182 ⇒ per 169 m of B, C is 13 m ahead; scale by 350/169 gives the same 350/13.

Common pitfalls

• Assuming margins scale linearly (31 vs. 18) without accounting for speed ratios.

Final Answer
350/13 m (≈ 26.92 m)