1. ## Clock This!

Not originals but fun, nonetheless.

1#
A clock with a sweep second hand is set with all three hands aligned at Noon, and the clock is started and run until Midnight. During the 12-hour period given, when were the three hands of the clock aligned with each other?

2#
The clock in the church tower takes seven seconds to strike 7 o'clock. How long will it take to strike eleven o'clock?

3#
What common event occurs regularly every 65 minutes 27.3 seconds?

4#
-------T H I S
--------- I S A
---G R E A T
------T I M E
========+
W A S T E R

------ used to align the text correctly.

5#
At what time, between the hours of 12:00 noon and 1:00 p.m. would the angle between the hour hand and the minute hand of a continuously driven clock be exactly 180 degrees?

6#
My 12 hour watch is 1 second fast per hour and your 12 hour watch is 1.5 seconds slow per hour. Right now they show the same time. When will they show the same time again? When will they show the same correct time again?

2. ## Re: Clock This!

2# <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">I think you want 11 and 2/3 seconds as reply (10 * 7/6) but strictly speaking the problem can't be solved since we don't know how long one "strike" lasts.</span hide>

3. ## Re: Clock This!

2 <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">7/6 * 10 = 11 2/3 seconds</span hide>

4. ## Re: Clock This!

3# <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">The hour hand and the minute hand of the clock are exactly aligned.</span hide>

5. ## Re: Clock This!

That's the solution I have.

Very true!

7. ## Re: Clock This!

5# <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">At 12:32:43.6 - the 32 minutes and 43.6 seconds is half the period of 65 minutes and 27.3 seconds from #3</span hide>

8. ## Re: Clock This!

#1 <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">12:00:00
13:05:27
14:10:55
15:16:22
16:21:49
17:27:16
18:32:44
19:38:11
20:43:38
21:49:05
22:54:33
24:00:00
</span hide>

9. ## Re: Clock This!

4#
<pre><span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold"> 5628
280
97405
5234
------+
108547</span hide></pre>

10. ## Re: Clock This!

<img src=/S/bash.gif border=0 alt=bash width=35 height=39> < During the 12-hour period given, when were the <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">three</span hide> hands of the clock aligned with each other?>

11. ## Re: Clock This!

4# and 5# correct. <img src=/S/thumbup.gif border=0 alt=thumbup width=15 height=15>

12. ## Re: Clock This!

OY! Ok, so my previous post was #1a - the times when the hr and minute hands were aligned. Given that none of the minutes and seconds were the same in the times that I quoted, I would have to say that the <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">3</span hide> hands were aligned at <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">12:00:00 and 24:00:00</span hide> and at no other time.

However, given my time related track record (see <post#=500,859>post 500,859</post: >), I could easily be wrong.

13. ## Re: Clock This!

Sorry, Tim I assumed all the items in the list were your solutions. Pick any prize you desire, in recompense.

14. ## Re: Clock This!

No, you were right to <img src=/S/bash.gif border=0 alt=bash width=35 height=39> me before as all times in my earlier post were my (incorrect) solution. After, picking myself off the floor, I saw the errors of my ways and ...

15. ## Re: Clock This!

6# <span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">720 days before they show the same time again; 3600 days before they both show the correct time again.</span hide>

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