Question 1092287
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I just solved another word clock problem at the link

<A HREF=https://www.algebra.com/algebra/homework/Finance/Finance.faq.question.1092284.html>https://www.algebra.com/algebra/homework/Finance/Finance.faq.question.1092284.html</A>


https://www.algebra.com/algebra/homework/Finance/Finance.faq.question.1092284.html


I explained there the theory behind clock problems, and I will use it here without repeating.
So I assume that you just read that solution and are familiar with the theory.



<pre>
To ask "what is the true time ?" in this situation is the same as to ask:
  

     At what time between 2:00 pm  and 3:00 pm the angle between the minute and the hour hands is exactly 30 degrees ?  

         ( 30 degrees  correspond to 5 minutes, 1/12 of the full revolution of the minute hand )


And the answer to it is the solution of this equation:

{{{(60 + (6/12)*t) - 6t}}} = 30.        (! 6t is the angular position of the minute hand measured in degrees from the "vertical up" position;
                            ( (60 + (6/12)*t) is the position of the hour hand measured in degrees from the "vertical up" position).


Or, which is the same,

{{{(60 + t/2)-6t}}} = 30.

Simplify and solve:

60 - 0.5t - 6t = 30  ====>  5.5t = 60 - 30  ====>  5.5t = 30  ====>

t = {{{30/5.5}}} = 5.(45) = 5 minutes and 27.(27) seconds = 5 minutes and 27.(27) seconds (approximately).


Here the record 5.(45)  means 5 followed periodical decimal fraction with the period 45;
                27.(27) means 27 followed periodical decimal fraction with the period 27.
</pre>

<U>Answer</U>.  The true time is 2 hours 5 minutes and 27.(27) seconds.



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