Question

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 будет день недели? ( Бассейн работает все дни)

Answer 1

НОК(3,4,5)=60
Друзья встретятся через 60 дней и это будет пятница (через 56 дней будет понедельник,57-вторник,58-среда,59-четверг,60-пятница)

Answer 2

Question Analysis

The question is asking how many days it will take for Petya, Vasya, and Kolya to meet again at the swimming pool after meeting on Monday. It also asks for the day of the week when they will meet again.

Answer

To determine how many days it will take for Petya, Vasya, and Kolya to meet again at the swimming pool, we need to find the least common multiple (LCM) of the numbers 3, 4, and 5. The LCM represents the smallest number that is divisible by all three numbers.

The LCM of 3, 4, and 5 is 60 Therefore, it will take 60 days for Petya, Vasya, and Kolya to meet again at the swimming pool.

To determine the day of the week when they will meet again, we need to calculate the remainder when dividing 60 by 7 (the number of days in a week). The remainder will tell us how many days after Monday they will meet again.

60 divided by 7 equals 8, with a remainder of 4 This means that after 60 days, they will meet again on the fourth day after Monday, which is Friday.

So, Petya, Vasya, and Kolya will meet again at the swimming pool in 60 days, on a Friday.

Example Calculation

To find the LCM of 3, 4, and 5, we can use the prime factorization method:

- Prime factorization of 3: 3 = 3 - Prime factorization of 4: 4 = 2 * 2 - Prime factorization of 5: 5 = 5

To find the LCM, we take the highest power of each prime factor:

- LCM = 2 * 2 * 3 * 5 = 60

Therefore, the LCM of 3, 4, and 5 is 60.

To find the day of the week, we divide 60 by 7:

- 60 divided by 7 equals 8, with a remainder of 4.

Therefore, they will meet again on the fourth day after Monday, which is Friday.

References

-: Source: '3, 4, ... - ...'