In a 1000-meter race, A finishes 100 meters ahead of B. In an 800-meter race, B finishes 100 meters ahead of C. How many meters will A win by against C in a 600-meter race?

Explanation

When A runs 1000 meters, B covers 900 meters. Similarly, when B runs 800 meters, C runs 700 meters. Therefore, when B runs 900 meters, C covers (900 × 700) ÷ 800 = 787.5 meters. This means in a 1000-meter race, A beats C by (1000 - 787.5) = 212.5 meters. Hence, in a 600-meter race, A will beat C by (600 × 212.5) ÷ 1000 = 127.5 meters.