# How many times do the hands of a clock overlap in a day?

A Better Approach (with reasoning) There are 2 cases depending on the working of the watch. Case 1: the movement of the second, minute and hour hands are co…ntinuous (not step-wise or click-based) Answer is: the hour and minute hands overlap every hour. Case 2 (very unusual): the hour hand jumps from 1 to 2, 2 to 3, ... and so on, as soon as the minute hand crosses (or reaches 12) and the minute hand jumps from 1 to 2, 2 to 3, ... and so on, as soon as the second hand crosses (or reaches 12). Answer: every 65 minutes. Interviewers often expect this answer cos they do not think accurately. The exact times are: 0000 (12:00 AM) 0105 (01:05 AM) 0211 (02:11 AM) 0316 (03:16 AM) 0422 (04:22 AM) 0527 (05:27 AM) 0633 (06:33 AM) 0738 (07:38 AM) 0844 (08:44 AM) 0949 (09:49 AM) 1055 (10:55 AM) 1200 (12:00 PM) 1305 (01:05 PM) 1411 (02:11 PM) 1516 (03:16 PM) 1622 (04:22 PM) 1727 (05:27 PM) 1833 (06:33 PM) 1938 (07:38 PM) 2044 (08:44 PM) 2149 (09:49 PM) 2255 (10:55 PM) Reasoning for Case 1: ----------------------------- When do they overlap? At every (n + (n/11)) hours where n = 0, 1, 2, 3, ..., 24. How did I find this out? The following is the reasoning i used: At 0000, the hour and minute hands overlap. So number of overlaps now is 1. The minute hand races away and never again overlaps during the next one hour. Now, the minute hand moves at 360o/hour and the hour hand moves at 30o/hour. At 0100, the hour hand would be the 1 mark (or 30o from the 12 mark) and the minute hand would be at the 12 mark. Starting at this position (at 0100), they would overlap when the number of degrees moved by both the minute and the hour hand are the same. Let them overlap at some time, say T, then I can write them in equation form as: 30o + (30o)x(T) = (360o)x(T) How did I get to this equation? Note that, at 0100, when the minute hand starts moving from the 12 mark, the hour hand is already ahead of the minute hand by 30o. If the minute hand moves at a speed of 360o/hour, then in some time (T), it would cover (360o)(T) degrees. If the hour hand hand moves at a speed of 30o/hour, then in the same time (T), it would cover (30o)(T) degrees. Since the hour hand is already 30o ahead from the 12 mark, the total degrees covered by the hour hand from the 12 mark would then be (30o + the number of degrees covered in time T) which is (30o + (30o)x(T)). Now the condition when the two hands will overlap is that they should have covered the same number of degrees at a moment (or) No. of degrees covered by minute hand = No. of degrees covered by hour hand (or) 30o + (30o)x(T) = (360o)x(T) If you solve this equation to find the value of T, you would get 30o = (360o)x(T) - (30o)x(T) 30o = (360o - 30o) x T 30o = 330o x T (or) T = 30o/330o T = 1/11 At 0200, the hour hand would be the 2 mark (or 60o from the 12 mark) and the minute hand would be at the 12 mark. Starting at this position (at 0200), they would overlap when the number of degrees moved by both the minute and the hour hand are the same. Let them overlap at some time, say T, then I can write them in equation form as: 60o + (30o)x(T) = (360o)x(T) Solving this equation, you will the value of T = 2/11 At 0300, using the same reasoning (the hour hand at 90o past the 12 mark) and modifying the equation accordingly (90o + (30o)x(T) = (360o)x(T)), you would get the answer for T = 3/11. In general, the value for T for every hour is T = n/11 where n = 0, 1, 2, 3, ..., 24. So the exact time when the two hands overlap can be written as: the hour (n) + the time taken during that hour (T) (or) n + n/11 where n = 0, 1, 2, 3, ..., 24. AM 12:00 1:05 2:11 3:16 4:22 5:27 6:33 7:38 8:44 9:49 10:55 PM 12:00 1:05 2:11 3:16 4:22 5:27 6:33 7:38 8:44 9:49 10:55 22 is correct. The hands overlap about every 65 minutes, not every 60 minutes. In a day, the hands would only overlap 22 times, as illustrated in the table above. I would propose that the hands always overlap, as they're both attached at the center of the dial. If you didn't want to be facetious (or, at least, less facetious), you would still have to ask how many hands were on the clock. It may have a second hand, for example, or be digital (no hands at all).

# What is the speed of a clock's second hand?

A clock's second hand makes one complete revolution each minute. Thus, by definition, it is rotating at one revolution per minute or one RPM. That's its "rotational velo…city" and it is the same no matter how big or small the clock might be. The actual velocity that the tip of the second hand might trace out as it revolves around the center of the clock will vary with the length of the second hand. The longer the hand, the faster the tip moves around the circumference.

# How many times does the average person wash their hands a day?

The correct answer would be 3.

# How many times can you wash your hands per day?

As many times as you want...BUT no matter how long or how many times you wash your hands, it will always have germs and never be completely clean. The average time is 20 secon…ds. The average amount for ME is 5 times.

# How many times do the hands of a clock coincide in a day?

The hands of a clock coincide 11 times in every 12 hours (Since between 11 and 1, they coincide only once, i.e., at 12 o'clock). AM 12:00 1:05 2:11 3:16 4:22 5:27 …6:33 7:38 8:44 9:49 10:55 PM 12:00 1:05 2:11 3:16 4:22 5:27 6:33 7:38 8:44 9:49 10:55 The hands overlap about every 65 minutes, not every 60 minutes. The hands coincide 22 times in a day.

# What is the speed of a clock's minute hand?

it moves at one click every 60 seconds

# How many times are the hands of a clock at right angle in a day?

It's not 16 times! The answer is 44 times!

# How many times a day is the hour hand opposite the minute hand?

22 times a day (11 times every 12 hours) Approximate times: 12:32:43 1:38:10 2:43:38 3:49:05 4:54:32 6:00:00 7:05:27 8:10:54 9:16:21 10:21:49 11:27:16 (see… the related questions below)

# How many times a day does a person need to do hand washing?

A person does not "need" to wash their hands on a daily basis, but rather "should" wash their hands whenever circumstances dictate. These instances include: when your hands… are dirtybefore eating or touching food (like if you're helping cook or bake, for example)after using the bathroomafter blowing your nose or coughingafter touching pets or other animalsafter playing outsidebefore and after visiting a sick relative or friend So the conclusion is that, you need to wash your hands a lot. Probably every three to four hours or so.

# How many times will the hand on a clock overlap during a year?

8,760 (365 days) 24 * 365. 8,784 (366 days) 24 * 366..... I think, not sure. 8P

# How many times do the minute hand and the hour hand overlap?

Once per hour.

Answered

In Science

# How many times the minute hand of a clock rotates in a day?

60 times 24 = 1,440

Answered

In Geometry

# How many times do not a clock's hands overlap in a day?

Infinitely many. Unless you consider the Planck time as the smallest, indivisible unit of time so that time is not a continuous variable.

Answered

In Uncategorized

# How many times does the minute hand and the hour hand overlap in the 24-hour clock in a day?

Twenty-four times of course !

Answered

In Geometry

# How many times do a clock's three hands overlap in a day?

All 3 hands overlap 24 times a day.

Answered

In Geometry

# How many times do a clock's hands overlap in 1 day?

22 times