Question

На маяке установлены 3 лампы . Первая вспыхивает 1 раз в 6 секунд , 2 - 1 раз в 10 секунд , 3 - 1 раз в 15 секунд . в какой момент все 3 лампы вспыхнут одновременно ? через сколько секунд все 3 лампы вспыхнут в следующий раз ? решение нужно

Answer 1

Все 3 лампы вспыхнут одновременно в момент, равный наименьшему общему кратному. Для чисел 6, 10 и 15 НОК= 30. В следующий раз все лампы вспыхнут одновременно также через 30 секунд. 

Answer 2

Problem Analysis

We are given three lamps on a lighthouse, each with a different flashing pattern. Lamp 1 flashes once every 6 seconds, Lamp 2 flashes once every 10 seconds, and Lamp 3 flashes once every 15 seconds. We need to determine when all three lamps will flash simultaneously and how many seconds it will take for them to flash simultaneously again.

Solution

To find the moment when all three lamps will flash simultaneously, we need to find the least common multiple (LCM) of the flashing intervals of the lamps. The LCM will give us the time at which all three lamps will flash together.

To find the LCM of 6, 10, and 15, we can use the prime factorization method or the division method. Let's use the division method, which is simpler for this case.

1. Start with the largest number, 15. 2. Check if it is divisible by 6. Since 15 is not divisible by 6, move to the next number. 3. Check if it is divisible by 10. Since 15 is not divisible by 10, move to the next number. 4. Check if it is divisible by 15. Since 15 is divisible by 15, we have found the LCM.

Therefore, the LCM of 6, 10, and 15 is 15 seconds. This means that all three lamps will flash simultaneously every 15 seconds.

To find the time it will take for all three lamps to flash simultaneously again, we need to find the LCM of 6, 10, and 15 again. Using the same method as before, we find that the LCM is still 15 seconds. Therefore, all three lamps will flash simultaneously every 15 seconds.

Answer

- All three lamps will flash simultaneously for the first time after 15 seconds. - All three lamps will flash simultaneously again after 15 seconds.

Please let me know if anything is unclear or if you need further assistance!