Question

Около школы останавливаются автобусы,следующие по трем разным маршрутам. Первый подходит к остановке через каждые 3 мин,второй -через каждые 6 мин,третий -через каждые 10 мин. В 7 ч на остановке стояли все три автобуса. В какое ближайшее время на остановке будут стоять снова три автобуса?В какое ближайшее время на остановке окажутся одновременно два автобуса? Помогите, пожалуйста решить уровнением

Answer 1

1000000000*1=1000000000

Answer 2

Problem Analysis

To solve this problem, we can use the concept of the least common multiple (LCM) to find the time at which all three buses will be at the stop together. Additionally, we can find the time at which two buses will be at the stop together by finding the LCM of the two bus intervals.

Time When All Three Buses Will Be at the Stop Again

The time when all three buses will be at the stop again can be found by calculating the LCM of the three intervals (3 minutes, 6 minutes, and 10 minutes).

The LCM of 3, 6, and 10 is 30 minutes. Therefore, all three buses will be at the stop together again in 30 minutes.

Time When Two Buses Will Be at the Stop Together

To find the time when two buses will be at the stop together, we can calculate the LCM of the intervals of the two buses.

- LCM of 3 and 6 is 6 minutes. Therefore, two buses will be at the stop together again in 6 minutes. - LCM of 3 and 10 is 30 minutes. Therefore, two buses will be at the stop together again in 30 minutes. - LCM of 6 and 10 is 30 minutes. Therefore, two buses will be at the stop together again in 30 minutes.

Hence, the next time when two buses will be at the stop together is 6 minutes.

Conclusion

- The next time when all three buses will be at the stop together is 30 minutes. - The next time when two buses will be at the stop together is 6 minutes.