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OPM 2006 Problem 1

  • Final day 1

Alexandre and Herculano are at Campanha station waiting for the train. To entertain themselves, they decide to calculate the length of a freight train that passes through the station without changing its speed. When the front of the train passes them, Alexandre starts walking in the direction of the train's movement and Herculano starts walking in the opposite direction. The two walk at the same speed and each of them stops at the moment they cross the end of the train. Alexandre walked 4545 meters and Herculano 3030 . How long is the train?

Dataset text AI-MO AoPS. Quoted with source.

Official text: Portuguese Mathematical Olympiad 2006 official paper, page 1.

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