At what time between 5 and 6 o' clock the hands of the clock be 3 minutes apart ?

The minute hand moves 12 times as fast as the hour hand. The minute hand covers the entire clock face (360 degrees) in 60 minutes, while the hour hand covers 30 degrees (1/12 of the clock face) in the same time.

So, in one minute, the minute hand moves 360/60 = 6 degrees, and the hour hand moves 30/60 = 0.5 degrees. The relative speed of the minute hand with respect to the hour hand is therefore 6 - 0.5 = 5.5 degrees per minute.

We want to find a time between 5 and 6 o'clock when the hands are 3 minutes apart. Since each minute on the clock face corresponds to 6 degrees (360 degrees / 60 minutes), a 3-minute gap corresponds to an 18-degree gap (3 minutes * 6 degrees/minute).

We can set up the equation 5.5t = 150 + 18, where t is the time in minutes past 5 o'clock. The 150 comes from the fact that at exactly 5 o'clock, the hands are 150 degrees apart (30 degrees * 5).

Solving for t gives t = (150 + 18) / 5.5 = 30.5454 minutes.

So, the hands are 3 minutes apart at approximately 30.55 minutes past 5, or at about 5:31.

The minute hand moves 12 times as fast as the hour hand. This means that for every minute, the minute hand moves 12 minutes on the clock face, while the hour hand moves 1 minute.

At 5 o'clock, the hands are 25 minutes apart. The minute hand must catch up to the hour hand for them to be 3 minutes apart. This means the minute hand must move 22 minutes on the clock face.

Since the minute hand moves 12 times as fast as the hour hand, it will take 22/11 = 2 minutes for the minute hand to catch up to the hour hand.

Therefore, the hands will be 3 minutes apart at 5:02.

The minute hand moves 12 times faster than the hour hand. So, let's assume that the minute hand has moved 'm' minutes when the two hands are 3 minutes apart.

Since the minute hand moves 12 times faster than the hour hand, the hour hand will have moved 'm/12' minutes.

The time is somewhere between 5 and 6 o'clock, so the hour hand starts at the 25 minute mark (5*5 = 25). Therefore, the position of the hour hand when the two hands are 3 minutes apart is 25 + m/12.

The position of the minute hand when the two hands are 3 minutes apart is just 'm'.

We know that the two hands are 3 minutes apart, so we can set up the following equation:

25 + m/12 = m + 3

Solving for 'm' gives us m = 33.6 minutes.

Therefore, the hands of the clock are 3 minutes apart at approximately 33.6 minutes past 5, or at about 5:34.

The minute hand moves 12 times as fast as the hour hand.

1. At 5 o'clock, the minute hand is at 12 and the hour hand is at 5. The minute hand needs to catch up to the hour hand for them to be 3 minutes apart.

2. Each minute on the clock represents 5 minutes. So, when we say the hands are 3 minutes apart, they are actually 15 minutes apart on the clock face.

3. The minute hand moves 12 times faster than the hour hand, so it will take 15/11 minutes for the minute hand to catch up to the hour hand.

4. 15/11 minutes is approximately 1.36 minutes.

5. Therefore, the hands will be 3 minutes apart at approximately 5:01.36.

Please note that this is an approximate time. The exact time will depend on the specific speed of the clock's hands.

The minute hand moves 12 times as fast as the hour hand. This means that for every minute, the minute hand moves 12 degrees and the hour hand moves 1 degree.

At 5 o'clock, the hands are 25 minutes apart. To be 3 minutes apart, they need to close a gap of 22 minutes.

Since the minute hand moves 11 minutes (or degrees) more than the hour hand per minute, it will take 2 minutes for the minute hand to close each minute of the gap.

Therefore, it will take 22 minutes * 2 = 44 minutes to close the 22 minute gap.

So, the hands will be 3 minutes apart at 44 minutes past 5, or 5:44.

The minute hand moves 12 times as fast as the hour hand. So, let's assume the time is 5 hours and x minutes.

The minute hand will be at 12x and the hour hand will be at 60*5 + x.

We know that the two hands are 3 minutes apart. Therefore, the absolute difference between the two hands is 3 minutes.

So, |12x - (605 + x)| = 312.

Solving this equation, we get two values of x: 22 and 38.

Therefore, the hands of the clock will be 3 minutes apart at 5:22 and 5:38.