Beating distance from 1 km times: A runs 1 km in 3 min 10 s (190 s), and B runs 1 km in 3 min 20 s (200 s). Starting together for 1 km, by what distance does A beat B?

Introduction / Context:Given individual 1 km times, compute how far the slower runner has run when the faster finishes; the shortfall is the winning distance.

Given Data / Assumptions:A: 1000 m in 190 s; B: 1000 m in 200 s; uniform speeds.

Concept / Approach:At t = 190 s (A's finish), B's distance is (190/200)*1000. Margin is 1000 minus this distance.

Step-by-Step Solution:

Verification / Alternative check:Speeds are 1000/190 and 1000/200 m/s; proportional comparison yields the same 50 m difference.

Why Other Options Are Wrong:30/36/60 are typical distractors from ratio misapplication.

Common Pitfalls:Subtracting times instead of comparing distances at the same time instant.

Final Answer:50 m