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Stopping and Turning back hands of time


Best Answer Prime, 25 February 2013 - 08:46 PM

Spoiler for

 

I see, I mixed up the adavance of the hour hand with the elapsed time for each cycle. And I calculated period incorrectly for the second part in my previous post.

Still, after the corrections, I get a different answer. My hour and minute hands will meet a lot sooner.

 

Why rejecting the occurences where the clock hands meet at 12 in a mid-cycle?

I see nothing in the OP prohibiting that. In fact, the clock hands will meet again at 12 on a mid-cycle before they do so after a whole number of cycles.

 

Spoiler for actually, the answer is

Go to the full post


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19 replies to this topic

#1 TimeSpaceLightForce

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Posted 20 February 2013 - 08:44 PM

A peculiar Grandfather's clock has both its hour and minute hands 
running in proper rates. Starting at 12 o'clock both runs clockwise.
But the hour hand stops when the minute hand passes over it. 
And the minute hand turn its direction back when it is over the stopped 
hour hand causing the hour hand to run clockwise again.
gfc.jpg
 
How long will it take for both hands to be on 12 o'clock again?

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#2 BobbyGo

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Posted 20 February 2013 - 09:01 PM

 

A peculiar Grandfather's clock has both its hour and minute hands 
running in proper rates. Starting at 12 o'clock both runs clockwise.
But the hour hand stops when the minute hand passes over it. 
And the minute hand turn its direction back when it is over the stopped 
hour hand causing the hour hand to run clockwise again.
 
How long will it take for both hands to be on 12 o'clock again?

Spoiler for Possibly...


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#3 Rob_Gandy

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Posted 20 February 2013 - 09:07 PM

If I'm reading this right...

Spoiler for I'd say


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#4 CaptainEd

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Posted 20 February 2013 - 09:08 PM

I see the clock reads 10:12. Do we start now? Or do we start at 12:00?

 

Also, I'm a little unclear what happens when the minute hand and hour hand meet: (When you said the minute hand "passes over" the hour hand, I assume that the minute hand continues in its direction.)

 

* minute hand going clockwise (CW), hits moving hour hand--hour hand stops, minute hand continues CW

* minute hand going CW, hits stopped hour hand--hour hand starts, minute hand goes Counterclockwise (CCW)

* minute hand going CCW, hist moving hour hand--hour hand stops, minute hand continues CCW

* minute hand going CCW, hits stopped hour hand--hour hand starts, minute hand goes CW.


Edited by CaptainEd, 20 February 2013 - 09:14 PM.

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#5 bonanova

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Posted 20 February 2013 - 09:47 PM

I see the clock reads 10:12. Do we start now? Or do we start at 12:00?

 

Also, I'm a little unclear what happens when the minute hand and hour hand meet: (When you said the minute hand "passes over" the hour hand, I assume that the minute hand continues in its direction.)

 

* minute hand going clockwise (CW), hits moving hour hand--hour hand stops, minute hand continues CW

* minute hand going CW, hits stopped hour hand--hour hand starts, minute hand goes Counterclockwise (CCW)

* minute hand going CCW, hist moving hour hand--hour hand stops, minute hand continues CCW

* minute hand going CCW, hits stopped hour hand--hour hand starts, minute hand goes CW.

 

That is the way I read the OP Cap'n.

 

But it may be the case that a forward-moving minute hand stops the hour hand, while a backward-moving minute hand starts the hour hand again. I think one of these interpretations precludes and answer, and that might make the OP as it stands a double puzzle.


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#6 CaptainEd

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Posted 20 February 2013 - 09:57 PM

Tricky!

Spoiler for answer and explanation

Edit: I agree, Bonanova, I'm not totally clear on the mechanism. A third interpretation might be that the MH reverses whenever it hits the HH. I'll take one of Y-san's Excedrins...


Edited by CaptainEd, 20 February 2013 - 10:02 PM.

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#7 TimeSpaceLightForce

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Posted 21 February 2013 - 01:42 PM

@captainEd, the pic is not the start, both @ 12 o'clock is the start where the hands are moving clockwise, eventually the MH overtakes the HH causing it to stop but the MH keeps going until it reached the stopped HH again where then it reverses its direction (like bumping) while causing the HH to move again(resume running clockwise) . No double interpretations is intended here.


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#8 TimeSpaceLightForce

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Posted 21 February 2013 - 01:46 PM

If I'm reading this right...

Spoiler for I'd say


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#9 CaptainEd

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Posted 21 February 2013 - 03:49 PM

@captainEd, the pic is not the start, both @ 12 o'clock is the start where the hands are moving clockwise, eventually the MH overtakes the HH causing it to stop but the MH keeps going until it reached the stopped HH again where then it reverses its direction (like bumping) while causing the HH to move again(resume running clockwise) . No double interpretations is intended here.

OK, TSLF, thanks.

Spoiler for from both up to both up


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#10 TimeSpaceLightForce

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Posted 21 February 2013 - 05:18 PM

Spoiler for


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