Problem

Source: 2003 Estonia National Olympiad Final Round grade 11 p1

Tags: algebra



Juhan is touring in Europe. He stands on a highway and watches cars. There are three cars driving along the highway at constant speeds: an Opel and a Trabant in one direction and a Mercedes in the opposite direction. At the moment when the Trabant passes Juhan, the Opel and the Mercedes lie at equal distances from him in opposite directions. At the moment when the Mercedes passes Juhan, the Opel and the Trabant lie at equal distances from him in opposite directions. Prove that at the moment when the Opel passes Juhan, also the Mercedes and the Trabant lie at equal distances from him in opposite directions.