Question

Интервалы движения городских автобусов по трем маршрутам, проходящим через общую остановку, составляют 15, 20 и 24 мин соответственно. Сколько раз с 7ч 55 мин до 17ч 5 мин того же дняна этой остановке одновременно встречаются автобусы всех трех маршрутов, если одна из таких встреч происходит в 12ч 35 мин

Answer 1

НОК(15,20,24)=120 мин.=2ч
12ч.35мин.-7ч.55мин.=4ч 40мин. ; 4ч 40мин/2ч =2 раза+остаток
зн. встретятся 2 раза до 12ч 35 мин.
17ч 5мин-12ч 35мин.=4ч 30мин /2 = 2 раза+остаток
зн. встретятся 2 раза после 12ч 35 мин.
Итого 4 +1=5 раз

Answer 2

Calculating Bus Meeting Times

To calculate the simultaneous meeting times for all three bus routes at the common bus stop, we can use the concept of the least common multiple (LCM) of the intervals between the buses. The LCM of 15, 20, and 24 is 120 minutes. This means that every 120 minutes, the buses of all three routes will meet at the common bus stop simultaneously.

Given that one such meeting occurs at 12:35 PM, we can calculate the number of simultaneous meetings between 7:55 AM and 5:05 PM on the same day.

Calculating the Number of Simultaneous Meetings

To calculate the number of simultaneous meetings, we can find the number of 120-minute intervals between 7:55 AM and 5:05 PM.

First, let's convert the given times to minutes: - 7:55 AM = 475 minutes - 5:05 PM = 905 minutes

Now, we can find the number of 120-minute intervals between these times: 905 - 475 = 430 minutes The number of 120-minute intervals in 430 minutes is 430 / 120 = 3 with a remainder of 70 minutes.

This means that there are 3 full 120-minute intervals and an additional 70 minutes between 7:55 AM and 5:05 PM. Therefore, the buses of all three routes will meet simultaneously 3 times, and there will be an additional meeting when the 70 minutes elapse.

So, the buses of all three routes will meet simultaneously 4 times from 7:55 AM to 5:05 PM on the same day.

Answer: The buses of all three routes will meet simultaneously 4 times from 7:55 AM to 5:05 PM on the same day.