A Puzzle A Day: 2026-03-20

In a 100-meter race, Alice beats Bob by 10 meters. In another 100-meter race, Bob beats Carol by 10 meters. If Alice and Carol were to race in a 100-meter dash, assuming they maintain their consistent speeds, by how many meters would Alice beat Carol?

19 meters20 meters18 meters10 meters

Correct: 19 meters

Let A, B, and C represent the speeds of Alice, Bob, and Carol, respectively. From the first race: When Alice runs 100 meters, Bob runs 90 meters. This means their speeds are in the ratio A/B = 100/90 = 10/9. From the second race: When Bob runs 100 meters, Carol runs 90 meters. This means their speeds are in the ratio B/C = 100/90 = 10/9. Now, to find how Alice compares to Carol, we need to find the ratio of their speeds (A/C): A/C = (A/B) * (B/C) A/C = (10/9) * (10/9) A/C = 100/81 This ratio means that for every 100 meters Alice runs, Carol runs 81 meters. Therefore, in a 100-meter race, Alice would beat Carol by 100 - 81 = 19 meters.

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