Question

В морской порт теплоход Беларусь прибывает один раз в 12 дней, теплоход Минск один раз в 20 дней, а теплоход Алые паруса - один раз в 18 дней. В прошлый вторник все три теплохода были в этом порту. В какой день недели они в следующий раз вместе прибудут в этот порт ? По действиям.

Answer 1

Найдём наименьшее общее кратное :
12 = 2 * 2 * 3
20 = 2 * 2 * 5
18 = 2 * 3 * 3
НОК (12; 20; 18) = 2 * 2 * 5 * 3 * 3 = 180
Значит, в следующий раз теплоходы встретятся через 180 дней.
Неделя = 7 дней  ⇒  180 : 7 = 25 (ост. 5)
Вторник + 5 дней = воскресенье.
Ответ: теплоходы встретятся в воскресенье.

Answer 2

Calculation of the Next Arrival Date

To determine the next day of the week when all three ships will arrive together in the port, we need to find the least common multiple (LCM) of the arrival intervals for each ship.

The arrival intervals for the three ships are as follows: - The ship "Belarus" arrives once every 12 days. - The ship "Minsk" arrives once every 20 days. - The ship "Алые паруса" (Red Sails) arrives once every 18 days.

To find the LCM, we can calculate the product of the prime factors of each interval, taking the highest power of each prime factor that appears in any of the intervals.

The prime factors of each interval are as follows: - The prime factors of 12 are 2 and 3. - The prime factors of 20 are 2 and 5. - The prime factors of 18 are 2 and 3.

Taking the highest power of each prime factor, the LCM is calculated as follows: - The highest power of 2 is 2^2 = 4. - The highest power of 3 is 3^1 = 3. - The highest power of 5 is 5^1 = 5.

Therefore, the LCM of the arrival intervals is 4 * 3 * 5 = 60 days.

Now, we need to determine the day of the week when the three ships will arrive together in the port. To do this, we need to know the day of the week when they last arrived together.

According to the given information, the three ships were last in the port on the previous Tuesday. To calculate the next arrival day, we need to add the LCM (60 days) to the previous Tuesday.

Adding 60 days to the previous Tuesday, we get the following calculation: - Tuesday + 60 days = Sunday

Therefore, the three ships will arrive together in the port on the next Sunday.

Answer: The three ships will arrive together in the port on the next Sunday.