Question

Улитка ползёт вокруг циферблата часов против часовой стрелки с постоянной скоростью. Она стартовала в 15:00 с отметки « 15 минут» и закончила полный круг ровно в 17:00. На каких отметках (в минутах) улитка в ходе своего движения встречалась с минутной стрелкой?Ответа три Ответы введите в произвольном порядке.

Answer 1

Ответ:

10, 50 и 30 минут

Объяснение:

1 встреча:

старт улитки с отметки "15 минут", т. е. с числа 3, а старт минутной стрелки в 15:00, т. е. с числа 12. Расстояние между этими числами 15 промежутков. t=S/V t=15/1,5=10 (минут) – произойдёт первая встреча после старта. Минутная стрелка будет на числе 2, а это отметка "10 минут".

2 встреча:

Улитка будет двигаться против часовой стрелки и встретиться с минутной через 60/1,5=40 минут, а минутная стрелка в этот момент будет на отметке 10+40=50минут.

3 встреча:

Потом встреча состоится ещё через 40 минут, когда минутная стрелка будет находиться на отметке 30 минут, т.е. от отметки 50 минут(на часах это число 10) до 1 часа (число 12) пройдет 10 минут и + ещё 30 минут (число 6).

Answer 2

Problem Analysis

We are given that a snail is crawling around a clock dial in a counterclockwise direction at a constant speed. The snail starts at the "15 minutes" mark and completes a full circle exactly two hours later, at 17:00. We need to determine the positions (in minutes) where the snail intersects with the minute hand during its movement.

Solution

To solve this problem, we need to calculate the number of minutes that have passed since the snail started crawling at 15:00 until it completes a full circle at 17:00. We can then find the positions where the snail intersects with the minute hand by finding the corresponding minute marks on the clock dial.

Let's break down the problem step by step:

1. Calculate the total time elapsed in minutes from 15:00 to 17:00: - The snail starts at 15:00, which is equivalent to 900 minutes (15 * 60). - The snail completes a full circle at 17:00, which is equivalent to 1020 minutes (17 * 60). - The total time elapsed is 1020 - 900 = 120 minutes.

2. Calculate the number of intersections with the minute hand: - The minute hand completes a full circle every 60 minutes. - Divide the total time elapsed (120 minutes) by 60 to find the number of full circles completed by the minute hand. - The snail intersects with the minute hand at the same positions every 60 minutes. - Therefore, the snail intersects with the minute hand twice during its movement.

3. Calculate the positions where the snail intersects with the minute hand: - The snail starts at the "15 minutes" mark, which is equivalent to 15 minutes. - The first intersection occurs after 60 minutes, at the "15 minutes" mark again. - The second intersection occurs after another 60 minutes, at the "15 minutes" mark for the third time.

Therefore, the snail intersects with the minute hand at the "15 minutes" mark three times during its movement.

Answer

The snail intersects with the minute hand at the "15 minutes" mark three times during its movement.

Note: The answer is based on the given problem statement and assumes that the snail's movement is continuous and uninterrupted.