Question

Через остановку проходят автобусы,идущие по трем маршрутам. один из них подходит к остановке через каждые 3 минуты,другой- через каждые 6 мин,третий- через каждые 10 мин. В 8.45 мин к остановке одновременно подошли все три автобуса. в какое ближайшее время там снова окажутся три автобуса? В какое ближайшее время к остановке подъедут два автобуса?

Answer 1

НОК (3,6,10) = 30  
Значит через 30 мин в 09:15 подойдут три автобуса.

НОК (3,6) = 6
через 6 мин в 08:51 подойдут два автобуса.

Answer 2

Три автобуса через 30минут
два автобуса через 6 минут

Answer 3

Problem Analysis

We are given that there are three buses that pass by a bus stop at different intervals: every 3 minutes, every 6 minutes, and every 10 minutes. At 8:45 AM, all three buses arrived at the bus stop simultaneously. We need to determine the nearest time when three buses will be at the bus stop again, as well as the nearest time when two buses will arrive at the bus stop.

Solution

To find the nearest time when three buses will be at the bus stop again, we need to find the least common multiple (LCM) of the intervals at which the buses arrive. The LCM of 3, 6, and 10 is 30. Therefore, the three buses will be at the bus stop again in 30 minutes.

To find the nearest time when two buses will arrive at the bus stop, we need to find the LCM of the intervals at which any two buses arrive. The LCM of 3 and 6 is 6. Therefore, two buses will arrive at the bus stop in 6 minutes.

Answer

Therefore, the nearest time when three buses will be at the bus stop again is 8:45 AM + 30 minutes = 9:15 AM. The nearest time when two buses will arrive at the bus stop is 8:45 AM + 6 minutes = 8:51 AM.