Question 1091616
.
<pre>
Let the current time under the question be 9 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  {{{(t/60)*2pi}}}  radians, counting from it vertical position at 9:00 am.

     *** Minute hand makes its full revolution of  {{{2pi}}} radians in 60 minutes. ***


The hour hand at this moment is at the angular position  {{{(3/4)*2pi + (1/12)*(t/60)*2pi}}} radians, counting from its vertical position at midnight.

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


Three minutes ago the minute hand was in position of  {{{(t/60)*2pi - (3/60)*2pi}}}  radians.


In four minutes the hour hand will be in position of  {{{(3/4)*2pi + (1/12)*(t/60)*2pi + (1/12)*(4/60)*2pi}}} radians.


Therefore, the governing equation is 


{{{(t/60)*2pi - (3/60)*2pi}}} = {{{(3/4)*2pi + (1/12)*(t/60)*2pi + (1/12)*(4/60)*2pi - pi}}}.


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

          The rest is just arithmetic. 


As the first step, cancel {{{2pi}}} in both sides and multiply by 60 both sides. You will get

t - 3 = {{{45 + (t/12) + (4/12) - 30}}}  ====>

{{{t - t/12}}} = {{{45 + (4/12) - 30 + 3}}}  ====>  {{{(11/12)*t}}} = {{{18}}} {{{4/12}}} = {{{18}}} {{{1/3}}} = {{55/3}}}  ====>

t = {{{12/11}}}.{{{55/3}}} = 20 minutes
</pre>

<U>Answer</U>.  The current time is 9:20 am.



&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;******************
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;***** SOLVED *****
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;******************



To get familiar with the subject, see the lesson

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

in this site.



Also, &nbsp;you have this free of charge online textbook in ALGEBRA-I in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.


The referred lesson is the part of this online textbook under the topic 
"<U>Travel and Distance problems</U>".