A can run 22.5 m while B runs 25 m (same time). In a 1 km race, by how many metres does B beat A?

Problem restatementGiven a constant-time distance ratio, find B's winning margin in a 1000 m race.

Given data

• v_A : v_B = 22.5 : 25 = 9 : 10.

Concept/ApproachIn the time B finishes 1000 m, A covers (9/10) of that distance.

Step-by-step calculation A's distance when B finishes = (9/10) × 1000 = 900 m Winning margin = 1000 − 900 = 100 m

Verification/AlternativeScale the 9:10 ratio to 900:1000; the difference is the margin.

Final Answer100 m