<PRE><B>Question 1117661</B>
&lt;br&gt;
The responses from the other tutors show a perfectly good algebraic solution to your problem.&lt;br&gt;
Here is another solution method that I like to use for this kind of problem.&lt;br&gt;
The hour hand makes 1 revolution every 12 hours; the minute hand makes 12 revolutions every 12 hours.&lt;br&gt;
So there are 11 times in every 12-hour period when the hour and minute hands are pointing in the same direction.&lt;br&gt;
Since both hands move at constant rates, the times when the hands are pointing in the same direction will be separated by 12/11 hours.&lt;br&gt;
The two hands are pointing in the same direction at 12 o&#39;clock.&lt;br&gt;
The time between 8 and 9 o&#39;clock when the hands are pointing in the same direction is 8*(12/11) hours after 12 o&#39;clock.&lt;br&gt;
8*(12/11) hours = 8  and 8/11 hours
8/11 hours = 480/11 minutes = 43 7/11 minutes
7/11 minutes = 420/11 seconds = 38 2/11 seconds&lt;br&gt;
The two hands are pointing in the same direction at 8:43:38 2/11</PRE>