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### 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/
```
Associated Topics:
High School Basic Algebra
Middle School Algebra

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