Question 1092286
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<pre>
Let the current time under the question be 3 hours and "t" minutes, where t is the real number, so t can be fraction of minutes and seconds.


The minute hand is at angular position  of  {{{(360/60)*t}}} = 6t degrees, counting from its position "vertically up" at 3:00 pm.

     *** Minute hand makes its full revolution of  360 degrees in 60 minutes. ***


The hour hand at this moment is at the angular position  {{{90 + (1/12)*(360/60)*t}}} degrees, counting from its position "vertically up" at noon.

     *** Hour hand has the angular velocity 12 times less than the minute hand: it is 12 times slower. ***


Three minutes from now the minute hand will be in position of  {{{(360/60)*t + (360/60)*3}}}  degrees.


Nine minutes ago the hour hand was in position of  {{{90 + (1/12)*(360/60)*t - (1/12)*(360/60)*9}}}  degrees.


Therefore, the governing equation is 


{{{(360/60)*t + (360/60)*3}}} = {{{90 + (1/12)*(360/60)*t - (1/12)*(360/60)*9}}} + 180  degrees.


          The major part is done: the equation/the model is set up.

          The rest is just arithmetic. 


Simplify this equation

6t + 18 = {{{90 + (1/12)*6t - (1/12)*6*9 + 180}}}  ====>

{{{6t - t/2}}} = {{{90 - (9/2) + 180 - 18}}}  ====>  {{{(11/2)*t}}} = {{{247}}}{{{1/2}}}  = {{{495/2}}} ====>

t = {{{495/11}}} = 45 minutes
</pre>

<U>Answer</U>.  &nbsp;The current time is &nbsp;3:45 pm.



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