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Exercise 6, 2015-2016 second edition

Exercise 6, 2015-2016 second edition

Nick, Normen, Lennart and Maschja are participating in the International Math Olympiad. They are flying from Schiphol to Hong Kong, where the Olympiad is taking place. Everybody hands in his or her luggage at the check-in desk. Nick has a blue suitcase, Lennart a yellow one, Maschja a green one and Normen’s suitcase is red. The system for transporting luggage to the correct airplanes at Schiphol is an impressive network of different carousels. Every carousel has its own constant speed, but the carousels do not necessarily have the same speeds. Below you can find a snapshot of the suitcases of Nick, Normen, Lennart and Maschja in the carousel network.

The carousels appear to overlap, but they are actually situated above each other. By coincidence, for different values of constant speeds of these four carousels, the following is happening:

  1. There is a moment when the green and the yellow suitcases are exactly above each other.
  2. There is a moment when the green and the blue suitcases are exactly above each other.
  3. There is a moment when the green and the red suitcases are exactly above each other.
  4. There is a moment when the yellow and the red suitcases are exactly above each other.
  5. There is a moment when the yellow and the blue suitcases are exactly above each other.

Exercise

Show that there is a moment in time when the blue and the red suitcases are exactly above each other.