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MathNet 2010 — Part 02 Question 10

Math Olympiad Vault · MathNet 2010 — Part 02

Question 10

Ada and Luisa train every day, each of them always with the same speed, for the big race that will take place at the end of the year at school. Training starts at point $A$ and ends at point $B$, distant $3000~\mathrm{m}$. They depart at the same moment, but when Luisa finishes the race, there is still a need for $120~\mathrm{m}$ for ADA to reach point $B$. Yesterday, Luisa gave Ada a chance: "We left at the same time, but I leave a few meters before point A to get together." How many meters before point $A$ should Luisa leave to get along with Ada?