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## #1 2012-12-31 00:28:57

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,856
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### Clock Problem

Question 1: How to find the angle between the two hands of the clock at a given time?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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## #2 2012-12-31 00:45:48

anonimnystefy
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From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

### Re: Clock Problem

Hi Agnishom

The angle is |h*30°-(m/2)*11°-(s/120)*11°|

Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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## #3 2012-12-31 01:51:45

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,856
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### Re: Clock Problem

Sorry, it had been too stupid question

A clock is set right at 7 am. The clock gains 10 minutes in 24 hrs. What will the approximate time when the clock indicates 1 pm on the following day?

Is it 12:47:30 pm?

Last edited by Agnishom (2012-12-31 01:53:18)

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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## #4 2012-12-31 02:03:09

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

### Re: Clock Problem

That is correct.

Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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## #5 2012-12-31 02:13:54

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,856
Website

### Re: Clock Problem

Now, how do I show that the hands of the clock come in right angles 22 times?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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## #6 2012-12-31 02:17:33

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

### Re: Clock Problem

They do not. They are at right angles much more times. 46 times, I would say...

Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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## #7 2012-12-31 02:26:57

Agnishom
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From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,856
Website

### Re: Clock Problem

Then 22 is the number of what?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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## #8 2012-12-31 02:31:52

bob bundy
Registered: 2010-06-20
Posts: 8,354

### Re: Clock Problem

Maybe that is for 90 measured clockwise (the rest 270)  ?

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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## #9 2012-12-31 02:36:38

bob bundy
Registered: 2010-06-20
Posts: 8,354

### Re: Clock Problem

Changed my mind.  I think it is 22.

00.15
0045
01.15 and a bit
01.45 and a bit
.......

2 per hour

but as the hour hand advances you loose the last hour

so 11 hours at 2 per hour.

Stefy:  Is your clock a 24 hour one?  ie 23 x 2 = 46

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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## #10 2012-12-31 04:13:53

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

### Re: Clock Problem

Actually, it is neither. We need to be given a time period on which we count the right angles...

Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

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## #11 2012-12-31 05:32:36

scientia
Member
Registered: 2009-11-13
Posts: 224

### Re: Clock Problem

I think the problem is for a 12-hour period. The simplest way is to count how many times the hands are at right angles in every hourly.

00:00 to 01:00  2
01:00 to 02:00  2
02:00 to 03:00  2 (including 3 o'clock)
03:00 to 04:00  1
04:00 to 05:00  2
05:00 to 06:00  2
06:00 to 07:00  2
07:00 to 08:00  2
08:00 to 09:00  2 (including 9 o'clock)
09:00 to 10:00  1
10:00 to 11:00  2
11:00 to 12:00  2

The hands are at right angles twice every hourly except for the hours 03:0004:00 and 09:0010:00. So it's 22 times every twelve hours.

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## #12 2012-12-31 06:34:26

scientia
Member
Registered: 2009-11-13
Posts: 224

### Re: Clock Problem

Oh, here's the math.

The angular velocity of the minute hand is 6° per minute and that of the hour hand 0.5° per minute. The difference in their angular velocities is therefore 5.5° per minute. Starting at twelve o'clock, the time taken for the hands to be first at right angles with each other is 90/5.5 minutes. Thereafter the minute hand has to turn through 180° to be next at right angles with the hour hand; the time taken for this is 180/5.5 minutes. If
is the time in minutes at which the hands are perpendicular for the
th time after twelve o'clock, we have the formula:

There are 720 minutes in half a day. The largest integer

for which
is
.

Happy New Year!

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## #13 2012-12-31 06:53:27

scientia
Member
Registered: 2009-11-13
Posts: 224

### Re: Clock Problem

And these are the times at which the hands are perpendicular (using 12-hour notation):

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## #14 2012-12-31 17:36:47

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,856
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### Re: Clock Problem

Got it! Happy New Year!

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

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