Question

Два теплохода одновременно отправляются из одного порта по разным маршрутам. У одного рейс туда и обратно длится 35 дн., а у другого 45 дн.. Найди время, через которое теплоходы снова встретятся в порту?

Answer 1

Рейс у первого теплохода 1/35
Рейс у второго теплохода 1/45
 Общий знаменатель и  будет являться временем, через которое теплоходы встретятся в порту.
1/35+1/45=9/315+7/315=16/315 
Ответ: через 315 дней.

Answer 2

Problem Analysis

We are given two ships that depart from the same port and follow different routes. The first ship takes 35 days for a round trip, while the second ship takes 45 days for a round trip. We need to find the time at which the two ships will meet again at the port.

Solution

To find the time at which the two ships will meet again at the port, we need to find the least common multiple (LCM) of the two round trip durations.

The LCM of two numbers is the smallest number that is divisible by both numbers. In this case, the LCM will give us the number of days after which both ships will complete an integer number of round trips.

Let's calculate the LCM of 35 and 45 to find the time at which the two ships will meet again at the port.

Calculation

To calculate the LCM of 35 and 45, we can use the prime factorization method or the division method. Let's use the division method for simplicity.

1. Start by dividing the larger number (45) by the smaller number (35). - 45 ÷ 35 = 1 remainder 10

2. Divide the divisor (35) by the remainder (10). - 35 ÷ 10 = 3 remainder 5

3. Divide the previous remainder (10) by the current remainder (5). - 10 ÷ 5 = 2 remainder 0

4. The LCM is the product of all the divisors and the final remainder. - LCM(35, 45) = 35 × 3 × 5 × 2 = 210

Therefore, the two ships will meet again at the port after 210 days.

Answer

The two ships will meet again at the port after 210 days.