Question

Помогите решить задачу. Петя ходит в бассейн раз в 3 дня, Вася - раз в 4 дня, а Коля - раз в 5 дней. В понедельник они встретились в бассейне. Через сколько дней они встретятся снова? Какой это будет день недели. (Бассейн работает все дни недели)

Answer 1

Problem Analysis

To solve this problem, we need to find the number of days it will take for Petya, Vasya, and Kolya to meet again at the swimming pool. Petya goes to the pool every 3 days, Vasya goes every 4 days, and Kolya goes every 5 days. We also need to determine the day of the week when they will meet again.

Solution

To find the number of days it will take for them to meet again, we need to find the least common multiple (LCM) of 3, 4, and 5. The LCM is the smallest positive integer that is divisible by all three numbers.

The LCM of 3, 4, and 5 is 60. Therefore, they will meet again after 60 days.

To determine the day of the week when they will meet again, we need to consider the starting day. In this case, they met on a Monday. We can use the fact that there are 7 days in a week and divide the number of days by 7 to find the remainder. The remainder will tell us the number of days after Monday when they will meet again.

60 divided by 7 gives a remainder of 4. This means that they will meet again 4 days after Monday. Therefore, they will meet again on Friday.

Answer

They will meet again after 60 days on a Friday.

Note: The above solution is based on the assumption that the swimming pool operates every day of the week.