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        riddles >> easy >> Clock Angles
        
(Message started by: Benoit_Mandelbrot on Apr 28^th, 2004, 9:30am)

Title: Clock Angles
Post by Benoit_Mandelbrot on Apr 28^th, 2004, 9:30am

This is about analog clocks.

a) The time is 3:10. What is the smaller angle between the two hands?

b) Develop a formula to find the angle at any given time.

Title: Re: Clock Angles
Post by towr on Apr 28^th, 2004, 9:58am

::[hide]
for time XX:YY
angle = min( |30 XX - 5.5 YY| , 360-|30 XX - 5.5 YY| )
so 35 degrees for 3:10
[/hide]::

Title: Re: Clock Angles
Post by Icarus on Apr 28^th, 2004, 6:57pm

I don't think so! ::[hide]Since it is 10 after, the minute hand is pointing exactly at 2. The hour hand should be 1/6 of the way from 3 to 4. Each division is 20^o, so the separation should be (20+20/6) degrees = 23^o20'.[/hide]::

Title: Re: Clock Angles
Post by THUDandBLUNDER on Apr 28^th, 2004, 9:52pm

Quote:

Each division is 20^o

Hmm...

Title: Re: Clock Angles
Post by rmsgrey on Apr 29^th, 2004, 3:48am

Obviously Icarus uses the well known 18 hour clock!

Title: Re: Clock Angles
Post by Sameer on Apr 29^th, 2004, 8:13am

on 04/29/04 at 03:48:24, rmsgrey wrote:

Obviously Icarus uses the well known 18 hour clock!

Hehe ;D

Title: Re: Clock Angles
Post by jtrook on Apr 29^th, 2004, 10:08am

Towr, your solution is excellent. I searched for another formula to find the angle and every attempt lead me back to the same thing - the formula you posted. ;D

Title: Re: Clock Angles
Post by Benoit_Mandelbrot on Apr 29^th, 2004, 10:24am

Towr's solution is the correct one. The answer is ::[hide]35 degrees[/hide]::.

Title: Re: Clock Angles
Post by Icarus on Apr 29^th, 2004, 3:15pm

Sheesh! I had a rough day yesterday, but I didn't think I'd sunk that low! :-[

Title: Re: Clock Angles
Post by Sir Col on Apr 29^th, 2004, 4:43pm

Oh well, I'm sure that your low day indirectly lifted many of our mediocre days with a bit of a chuckle. I hope this day was better for you.

I feel like I could do with one of those 18 hour clocks somedays; imagine what I could do with an extra 12 hours per day! Then it would be just the small matter of slowing the earth's rotation to coincide.

Title: Re: Clock Angles
Post by Icarus on Apr 29^th, 2004, 6:16pm

Certain days (such as I have been having all week), do not need extended! Shortening would be much more appropriate! ;)

Title: Re: Clock Angles
Post by Sir Col on Apr 30^th, 2004, 4:55am

Good point!

Perhaps we could maintain the average of 24 hours per day, but make Monday to Friday last 4 hours 48 minutes each (24 hours in total), and split Saturday and Sunday equally between the remaining 144 hours. As we normally work around 8 hours of a 24 hour cycle, we could excuse the fact that we didn't turn up to work until late on "Tuesday" by boasting about working all through "Wednesay" and most of "Thursday" with only an hour lunch break. Surely that would entitle us to take the rest of the week off?

Title: Re: Clock Angles
Post by ljoynich on May 6^th, 2005, 12:23pm

Re analog clock angle for 3:10.

Every 5 minutes represents 30 degrees.
so when it's 10 minutes after the hour that = 30 degrees.

The hour hand will also move 1/12 of 30 degrees each 5 minutes.

So 2/12 x 30 = 5 degrees plus the 30 degrees = a total of 35 degrees. (A solution by one of my seventh grade students)