Question

Два теплоходи одночасно відправляються з одного порту за різними маршрутами. В одного рейс туди і назад триває 30 дн., а в іншого 40 дн. Знайди час, через який теплоходи знову зустрінуться в порту. Відповідь: теплоходи знову зустрінуться в порту через дн.

Answer 1

Ответ: через 120 днів теплоходи знову встрінуться в порту

Пошаговое объяснение:

Розкладемо на прості множники 30 і 40

30 = 2 * 3 * 5

40 = 2 * 2 * 2 * 5

НОК (30; 40) = 2 * 2 * 2 * 5 * 3 = 120

через 120 днів теплоходи знову зустрiнуться в порту.  

Answer 2

To find the time when the two ships will meet again in the port, we need to determine the least common multiple (LCM) of the two durations of their round trips.

Ship A takes 30 days for a round trip, while Ship B takes 40 days for a round trip.

The LCM of 30 and 40 will give us the time when both ships will have completed an integer number of round trips.

To find the LCM, we can use the prime factorization method or the division method. Let's use the division method for simplicity.

Division Method to Find LCM:

1. Write the two numbers (30 and 40) side by side. 2. Divide both numbers by the smallest prime number that divides at least one of them. In this case, the smallest prime number is 2. - 30 ÷ 2 = 15 - 40 ÷ 2 = 20 3. Repeat step 2 until both numbers are no longer divisible by 2. - 15 ÷ 3 = 5 - 20 ÷ 2 = 10 4. Repeat steps 2 and 3 with the next prime number, which is 3. - 5 ÷ 5 = 1 - 10 ÷ 2 = 5 5. Repeat step 4 until both numbers are no longer divisible by 3. - 1 is not divisible by 3. - 5 is not divisible by 3. 6. Repeat steps 4 and 5 with the next prime number, which is 5. - 1 is not divisible by 5. - 5 is divisible by 5. 7. The LCM is the product of all the divisors and the remaining numbers. - LCM(30, 40) = 2 × 2 × 3 × 5 = 60

Therefore, the two ships will meet again in the port after 60 days.

Answer: The two ships will meet again in the port after 60 days.