Question 1117661
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<pre>
I will count and compare the angles that the hour hand and the minute hand make with the direction "vertically up", 
which is their position at noon.


The hour hand rotates 360 degs in 12 hours; hence, its angular velocity is {{{360/(12*60)}}} = 0.5 degree per minute.


The minute hand rotates {{{360/60}}} = 6 degrees per minute; it is its angular velocity.


Let the current time is  8 hours and t minutes,  0 <= t <= 60.


The position of the hour hand is 8*30 + 0.5*t  degrees (counting from the direction "vertically up")).
The position of the minute hand is  6t degrees.


The positions coincide - it gives you an equation

    8*30 + 0.5t = 6t.


Simplify and solve for t:

    240 = 6t - 0.5t  ====>  5.5t = 240  ====>  t = {{{240/5.5}}} = 43.6363 . . . minutes = 43 minutes and 38 seconds.


<U>Answer</U>.  The time is  8 hours 43 minutes and 38 seconds.
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Solved.


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

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