3
Part of 1996 May Olympiad
Problems(2)
Natalia and Marcela counting numbers
Source: II May Olympiad (Olimpiada de Mayo) 1996 L2 P3
9/17/2022
Natalia and Marcela count by starting together at , but Marcela's speed is triple that of Natalia (when Natalia says her second number, Marcela says the fourth number). When the difference of the numbers that they say in unison is any of the multiples of , between and , Natalia continues counting normally and Marcela begins to count downwards in such a way that, at one point, the two say in unison the same number. What is said number?
algebranumber theory
2 cylindrical containers with water
Source: II May Olympiad (Olimpiada de Mayo) 1996 L1 P3
9/17/2022
and are two cylindrical containers that contain water. The height of the water at is cm and at , cm. Using a pump, water is transferred from to . It is noted that, in container , the height of the water decreases cm per minute and in it increases cm per minute. After how much time, since the pump was started, will the heights at and be the same?
algebra