IL-GILLIS 2016 Problem 1
Nina and Meir are walking on a km path towards grandma's house. They start walking at the same time from the same point. Meir's speed is km/h and Nina's speed is km/h.
Along the path there are several benches. Whenever Nina or Meir reaches a bench, they sit on it for some time and eat a cookie. Nina always takes minutes to eat a cookie, and Meir always takes minutes to eat a cookie, where is a positive integer.
It turns out that Nina and Meir reached grandma's house at the same time. How many benches were there? Find all of the options.
Dataset text AI-MO AoPS. Quoted with source.
Solutions
No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.