When Hands of a Clock Meet

Date: 8/29/96 at 17:41:27
From: Anonymous
Subject: When Hands of a Clock Meet

To the nearest second, what is the first time after 12:00 that the 
hour hand and the minute hand of a clock are together?

Thanks!

Date: 8/30/96 at 13:58:47
From: Doctor Tom
Subject: Re: When Hands of a Clock Meet

I won't give the answer, but here's a hint:

Obviously, they'll meet a bit after 1:00.  So if the answer is x 
minutes, the hour hand will have to move x minute marks and the minute 
hand will have to move x+60 minute marks, right?

The hour hand moves at 5 marks per hour, or 1/12 mark per minute, and 
the minute hand moves at 60 marks per hour, or 1 mark per minute.

Just write down the equations for the distances that the hour hand and 
minute hand move and set them equal.  When you solve, you'll get x.

-Doctor Tom,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/