Question 1195550
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It is now between 10:00-11:00 o'clock, and six minutes from now, 
the minute hand of a watch will be exactly opposite the place where the hour hand 
was three minutes ago. What is the exact time now?
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<pre>
Imagine wall clock and its clock face.

I will measure degrees in clockwise direction, starting from position 12:00 
(from direction vertically up).


Let "m" be the number of minutes after 10:00 under the problem's question
(notice that under this consideration, "m" is not necessary integer number: it can be a real number, actually).


The angle for the hour hand 3 minutes ago from now was  300 + {{{(360/(12*60))*(m-3)}}} = 300 + {{{(1/2)*(m-3)}}} degrees.

The angle for the minute hand 6 minutes from now will be  {{{(360/60)*(m+6)}}} degrees = 6(m+6) degrees.


Our equation to find "m" is

    300 + {{{(1/2)(m-3)}}} = 180 + 6(m+6).


Simplify

    600 - 360   = 12(m+6) - (m-3)

       240      = 12m + 72 - m + 3

       240      = 11m + 75
     
       240 - 75 = 11m

          165   = 11m

           m    = 165/11 = 15 minutes.


<U>ANSWER</U>  to the problem's question is  15 minutes after 10:00,  or  10:15.
</pre>

Solved, explained and completed.


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To see many other similar and different clock hand problems, &nbsp;look into the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/travel/Clock-problems.lesson>Clock problems</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/travel/Advanced-clock-problems.lesson>Advanced clock problems</A>

in this site.


Learn the subject from there.