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MathNet 2026 — Part 02 Question 24

Math Olympiad Vault · MathNet 2026 — Part 02

Question 24

Julian trains on a track of $3~\mathrm{km}$. He walks the first kilometer by walking, the second running, and the third on a bicycle. If he had traveled the entire track by bicycle, it would have taken 10 minutes less. Julian runs at twice the speed with which he walks, and rides a bicycle at triple the speed with which he walks. How long does Julian take to run $1~\mathrm{km}$?