What time between 4 and 5 o'clock will the hands of a clock be at right angle?(38 +2/11) min past 4(38 +2/11) min past 5(38 +5/11) min past 4(48 +2/11) min past 4

The hands of a clock are at right angles twice in every hour - once near the start of the hour and once near the end.

1. The first time the hands are at right angles is when the minute hand has moved 15 minutes ahead of the hour hand. This happens approximately 22 minutes into the hour. However, this is not between 4 and 5 o'clock.

2. The second time the hands are at right angles is when the minute hand is 15 minutes behind the hour hand. This happens approximately 38 minutes into the hour. So, the hands of the clock will be at right angles at approximately (38 + 2/11) minutes past 4.

3. The hands will not be at right angles at (38 + 2/11) minutes past 5, (38 + 5/11) minutes past 4, or (48 + 2/11) minutes past 4.

So, the correct answer is (38 + 2/11) minutes past 4.

The hands of a clock are at right angles twice in every hour - once near the start of the hour and once near the end.

1. The first time the hands are at right angles is when the minute hand has moved 1/4 of the way around the clock from the hour hand. This happens 1/4 of an hour, or 15 minutes, after the start of the hour.

2. The second time the hands are at right angles is when the minute hand has moved 3/4 of the way around the clock from the hour hand. This happens 3/4 of an hour, or 45 minutes, after the start of the hour.

So, between 4 and 5 o'clock, the hands of a clock will be at right angles at 15 minutes past 4 and 45 minutes past 4.

However, the exact times can be calculated as follows:

1. The minute hand is 12 times faster than the hour hand. So, in 60 minutes, the difference in speed between the two hands is 12 * 60 = 720 degrees.

2. A right angle is 90 degrees. So, the minute hand will be at a right angle to the hour hand 90/720 = 1/8 of an hour after the start of the hour. This is 60/8 = 7.5 minutes.

3. So, the first time the hands are at right angles is 4:00 + 7.5 minutes = 4:07.5.

4. The second time the hands are at right angles is 3/4 of an hour after the start of the hour. This is 60 * 3/4 = 45 minutes.

5. So, the second time the hands are at right angles is 4:00 + 45 minutes = 4:45.

Therefore, between 4 and 5 o'clock, the hands of a clock will be at right angles at 4:07.5 and 4:45.

The hands of a clock are at right angles twice in every hour - once near the start of the hour and once near the end.

1. First, we need to calculate the minute hand's position at 4 o'clock. At 4 o'clock, the minute hand is at 12 (or 0) and the hour hand is at 4.

2. The minute hand moves 12 times faster than the hour hand. So, in one minute, the minute hand moves 12 degrees and the hour hand moves 1 degree.

3. We want to find when the hands are 90 degrees apart. At 4 o'clock, the hands are 120 degrees apart (30 degrees per hour * 4 hours).

4. So, the hands will be 90 degrees apart 30 degrees later. Since the minute hand moves 12 times faster than the hour hand, it will take 30/11 minutes for the hands to be 90 degrees apart.

5. Therefore, the hands will be 90 degrees apart at (30/11) minutes past 4, or approximately (2 + 8/11) minutes past 4.

6. The hands will be 90 degrees apart again near the end of the hour. This will be 60 - (30/11) minutes past 4, or approximately (57 + 3/11) minutes past 4.

So, the hands of a clock will be at right angles at approximately (2 + 8/11) minutes past 4 and (57 + 3/11) minutes past 4.

The hands of a clock are at right angles twice in every hour. The first time is a little after half past the hour and the second time is a little before half past the next hour.

1. The minute hand moves 12 times faster than the hour hand. So, in 60 minutes, the minute hand gains 55 minutes on the hour hand.

2. To be at right angles, they must be 15 minutes apart.

3. The minute hand will be 15 minutes ahead of the hour hand 15/55 minutes after the hour, which is 16 4/11 minutes after the hour.

4. The minute hand will be 15 minutes behind the hour hand 45/55 minutes after the hour, which is 49 1/11 minutes after the hour.

So, between 4 and 5 o'clock, the hands will be at right angles at (16 4/11 + 460/11) minutes past 4, which is approximately 38 2/11 minutes past 4, and at (49 1/11 + 460/11) minutes past 4, which is approximately 48 2/11 minutes past 4.

Therefore, the correct answers are (38 +2/11) min past 4 and (48 +2/11) min past 4.

The hands of a clock are at right angles twice in every hour - once near the start of the hour and once near the end.

1. First, we need to calculate the minute hand's position at 4 o'clock. At 4 o'clock, the minute hand is at 12 (or 0) and the hour hand is at 4.

2. The minute hand moves 12 times faster than the hour hand. So, in t minutes, the minute hand will be t/5 hours ahead of the 4 o'clock position, and the hour hand will be t/60 hours ahead of the 4 o'clock position.

3. We want these two quantities to differ by 1/4 of an hour (a right angle), so we set up the equation t/5 - t/60 = 1/4 and solve for t.

4. Solving this equation gives t = 38 + 2/11 minutes.

So, the hands of the clock will be at right angles at (38 + 2/11) minutes past 4.

5. For the second time in the hour when the hands are at right angles, we want the minute hand to be 1/4 of an hour behind the hour hand. So, we set up the equation t/5 + 1/4 = t/60 and solve for t.

6. Solving this equation gives t = 48 + 2/11 minutes.

So, the hands of the clock will be at right angles for the second time at (48 + 2/11) minutes past 4.

Therefore, the hands of a clock will be at right angles at (38 + 2/11) minutes past 4 and (48 + 2/11) minutes past 4.