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Chase on an endless road



You and your friend are standing on a road which goes on forever in both directions. Your friend suggests a game of chase. Since you are faster, your friend will get a head start. Also, to make it more interesting than a simple Achilles vs Tortoise race, you will not know in which direction your friend takes off.

  • You move at constant speed x>1 m/s and your friend moves at constant speed 1 m/s.
  • Your friend gets a 1 hour head start.
  • Visibility is limited so you will not be able to see your friend from a distance.
  • You must not stray from the road, same goes for your friend.

Can you catch up to your friend? Does the answer depend on your speed x, and if so, what is the minimum x for which you can catch up? What is your strategy?

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