In a 200 m race, A beats B by 35 m or 7 seconds. What is A's time to finish the 200 m course?

Problem restatementA finishes 200 m when B is at 165 m (beaten by 35 m). The same margin corresponds to 7 seconds. Find A's finishing time for 200 m.

Given data

• Race length = 200 m.
• Margin: 35 m equals 7 seconds for B.

Concept/ApproachUse B's speed from the given margin-time, compute B's 200 m time, then subtract the 7 s lead to get A's time.

Step-by-step calculation B's speed = 35 ÷ 7 = 5 m/s B's 200 m time = 200 ÷ 5 = 40 s A's time = B's time − lead = 40 − 7 = 33 s

Verification/AlternativeAt 33 s, B covers 5 × 33 = 165 m, matching the 35 m deficit when A finishes.

Common pitfalls

• Interpreting 7 s as A's advantage in speed rather than time.
• Using 165 m for A by mistake; A runs the full 200 m.

Final Answer33 seconds