Question 1092284
<br>From the given information, we know, since the hour and minute hands move at uniform rates, that the minute hand and hour hand will be pointing in exactly the same direction 5 minutes from now.<br>
The minute hand makes 12 revolutions every 12 hours; the hour hand makes 1.  That means the minute and hour hands are pointing in the same direction 11 times every 12 hours.  Again since the hands both move at uniform rates, we know the interval between times when the hands point in the same direction is 12/11 hours.<br>
The minute and hour hands point in the same direction at 12:00.  So the time shortly after 2:00 when the hands align will be 24/11 hours after 12:00, or 2/11 hours after 2.<br>
2/11 hours = 120/11 minutes = 10  10/11 minutes.
10/11 minutes = 600/11 seconds = 54 6/11 seconds.
To the nearest second, the time shortly after 2 when the hands align is 2:10:55.<br>
So the current time is 5 minutes before that -- at 2:05:55.