Question

Коля разобрал часы со стрелками и неправильно их собрал: перепутал часовую стрелку с минутной, кроме того, они начали идти в обратную сторону. Коля запустил часы в полдень, выставив точное время. Сколько раз за период с 12:01 до 23:59 такие часы покажут правильное время? С РЕШЕНИЕМ!!!

Answer 1

Відповідь:

Покрокове пояснення:

Так как стрелки Коля перепутал, то за один час "часовая" стрелка пройдёт весь циферблат, а "минутная" перемистится на 5 мин назад, поэтому каждый час будет одно положение, которое совпадает с реальным временем -> за 12 часов наблюдения за часами 12 раз будет показано правильное время

Answer 2

Problem Analysis

Kolya disassembled a clock with hour and minute hands and reassembled them incorrectly. He swapped the hour hand with the minute hand and the clock started running in the opposite direction. Kolya set the clock to the exact time of noon (12:00 PM). The question is how many times between 12:01 PM and 11:59 PM the clock will show the correct time.

Solution

To solve this problem, we need to determine how many times the swapped hour and minute hands will align correctly between 12:01 PM and 11:59 PM.

Let's break down the problem into smaller steps:

1. Calculate the time it takes for the hour hand to complete one full revolution (360 degrees). The hour hand completes one full revolution in 12 hours or 720 minutes. 2. Calculate the time it takes for the minute hand to complete one full revolution (360 degrees). The minute hand completes one full revolution in 60 minutes. 3. Calculate the time it takes for the minute hand to catch up to the hour hand by one full revolution. This is the difference between the time it takes for the hour hand and the minute hand to complete one full revolution. In this case, it is 720 - 60 = 660 minutes. 4. Calculate the time it takes for the minute hand to catch up to the hour hand by one minute. This is the time it takes for the minute hand to cover the 660-minute difference. It is equal to 660 / 60 = 11 minutes. 5. Calculate the number of times the minute hand will catch up to the hour hand between 12:01 PM and 11:59 PM. This can be calculated by dividing the total time period (11 hours and 58 minutes) by the time it takes for the minute hand to catch up by one minute (11 minutes). The result is (11 * 60 + 58) / 11 = 71 times.

Therefore, the clock will show the correct time 71 times between 12:01 PM and 11:59 PM.

Note: This solution assumes that the clock hands move continuously without any pauses or interruptions.

Conclusion

Between 12:01 PM and 11:59 PM, the clock with the swapped hour and minute hands will show the correct time 71 times.

I hope this helps! Let me know if you have any further questions.