At what time between 2 and 3 o'clock will the hands of a clock be together?

The hands of a clock are together at 12 o'clock. After that, they are together every 65 minutes.

Step 1: Determine the time when the hands are together after 12 o'clock. This is 12 o'clock plus 65 minutes, which is 1:05.

Step 2: Determine the next time the hands are together. This is 1:05 plus 65 minutes, which is 2:10.

However, the question asks for the time between 2 and 3 o'clock. 2:10 is not between 2 and 3 o'clock, so we need to find the next time the hands are together.

Step 3: Determine the next time the hands are together. This is 2:10 plus 65 minutes, which is 3:15.

However, 3:15 is not between 2 and 3 o'clock. Therefore, the hands of the clock are not together between 2 and 3 o'clock.

The minute hand moves 12 times as fast as the hour hand. So, they are together every 65 minutes.

At 2 o'clock, the minute hand is at 12 and the hour hand is at 2. The minute hand has to make up that 20 minute gap.

Since the minute hand gains 10 minutes per hour (60 minutes) on the hour hand, it will take 2 hours (120 minutes) for the minute hand to gain 20 minutes on the hour hand.

However, we are only interested in the time between 2 and 3 o'clock.

So, we divide 20 minutes by 12 (since the minute hand moves 12 times as fast as the hour hand) to get approximately 1.67 minutes.

This means that the hands will be together at approximately 2:11.

The minute hand moves 12 times as fast as the hour hand. So, the two hands are together once every hour except between 11 and 12.

1. At 2 o'clock, the minute hand is at 12 and the hour hand is at 2. The minute hand has to make up that 20-minute gap.
2. Since the minute hand moves 12 times as fast as the hour hand, it takes 60/12 = 5 minutes for the minute hand to make up each "minute" of that gap.
3. Therefore, it will take 20 * 5 = 100 minutes for the minute hand to catch up to the hour hand.
4. But we're looking for the time between 2 and 3 o'clock, not the time after 2 o'clock. So, we need to convert 100 minutes into hours and minutes.
5. 100 minutes = 1 hour and 40 minutes.
6. Therefore, the hands will be together at 2:40.

The hands of a clock move at different speeds. The minute hand moves 12 times faster than the hour hand.

1. At 2 o'clock, the minute hand is at 12 and the hour hand is at 2. This means there is a 40-minute space between the two hands (each hour mark represents 5 minutes on a clock).

2. We know that the minute hand moves 12 times faster than the hour hand. So, to find out when the two hands will meet (be in the same place), we need to figure out when the minute hand will make up this 40-minute gap.

3. Since the minute hand moves 12 times faster, we divide the 40-minute gap by 12. 40/12 = 3.33 minutes.

4. This means that the hands will be together 3.33 minutes after 2 o'clock.

So, the hands of the clock will be together at approximately 2:20.