My Math Forum Clock Problem

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 March 24th, 2010, 02:44 PM #1 Member   Joined: Dec 2009 Posts: 66 Thanks: 0 Clock Problem "Find the number of minutes after 3:00 that the minute and hour hands of a clock will first form an angle of 154 degrees" I'm having a problem formatting this equation :/
 March 24th, 2010, 04:05 PM #2 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,853 Thanks: 1077 Math Focus: Elementary mathematics and beyond Re: Clock Problem Assuming the hour hand moves one 'tick' every 12 minutes and that there are 60 'ticks' on the clock you need to solve 6(M - (M/12 + 15)) = 154 (6 degrees per 'tick') for M.
March 24th, 2010, 07:19 PM   #3
Math Team

Joined: Dec 2006
From: Lexington, MA

Posts: 3,267
Thanks: 407

Re: Clock Problem

Hello, Recipe!

greg1313 is absolutely correct!

Here's my approach . . . along with my baby-talk thought processes.

Quote:
 Find the number of minutes after 3:00 that the minute hand and hour hands of a clock will first form an angle of 154 degrees.

$\text{The minute hand moves }360^o\text{ in 60 minutes.}$
[color=beige]. . [/color]$\text{Its angular speed is: }\:6^o\text{ per minute.}$
$\text{Starting at }0^o\text{, in }t\text{ minutes, its position will be: }\:M \;=\;6t\text{ degrees.}$

$\text{The hour hand moves }360^o\text{ in 12 hours (720 minutes).}$
[color=beige]. . [/color]$\text{Its angular speed is: }\:\frac{1}{2}^o\text{ per minute.}$
$\text{Starting at }90^o\text{, in }t\text{ minutes, its position will be: }\:H \;=\;90\,+\,\frac{1}{2}t\text{ degrees.}$

$\text{When will }M\text{ be }154^o\text{ ahead of }H?$

$\text{There is our equation!} \;\;\;\cdots\;\;\;6t \;=\;90\,+\,\frac{1}{2}t \,+\,154 \;\;\;\Rightarrow\;\;\;\frac{11}{2}t \:=\:244$

$\text{Therefore: }\:t \;=\;\frac{488}{11} \;=\;44\frac{4}{11}$$\text{ minutes.}$

 March 25th, 2010, 01:54 PM #4 Member   Joined: Dec 2009 Posts: 66 Thanks: 0 Re: Clock Problem Thank you both!
 March 26th, 2010, 12:38 PM #5 Global Moderator   Joined: Dec 2006 Posts: 19,511 Thanks: 1743 In LaTeX, the degrees symbol is best achieved using ^\circ rather than ^o, e.g., $^{154^\circ}$ instead of $^{154^o.}$
 March 26th, 2010, 01:20 PM #6 Math Team   Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 407 Re: Clock Problem I've used both:[color=beige] .[/color]^\circ[color=beige] .[/color]and[color=beige] .[/color]^o $\text{The difference is: }\:30^{\circ}\:\text{ and }\:30^o$ Guess which one I prefer to type?

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