# GRE Math : How to find the distance between clock hands

## Example Questions

### Example Question #3 : How To Find The Distance Between Clock Hands

A clock has two equally long hands on it, each measuring  inches. If the minute hand is directly on  and the hour hand is directly on , what is the distance between the two hands?

Explanation:

Our clock looks roughly like this:

Now, between every number on the clock, there are  or  degrees. Therefore, from  to , there are  degrees. To find the arc length, you use the equation:

Now, we know:

We know that . Therefore, we can write our equation:

### Example Question #5 : How To Find The Distance Between Clock Hands

A clock has two equally long hands on it, each measuring  inches. If the minute hand is directly on  and the hour hand is directly in the middle of  and , what is the distance between the two hands?

Explanation:

Our clock looks roughly like this:

Now, between every number on the clock, there are  or  degrees. We have a little trickier math to do, however. Let's subdivide the clock into  subsections instead. Each of these will have  degrees. Now, between  and , there are  such subsections. Since the hour hand is directly in the middle of  and , there is one more such subsection. Therefore, we have  total subsections or  degrees. To find the arc length, you use the equation:

Now, we know:

We know that .  Therefore, we can write our equation:

### Example Question #4 : How To Find The Distance Between Clock Hands

A clock has two equally long hands on it, each measuring  inches and extending to the edge of the clock. If the minute hand is directly on  and the hour hand is directly on , what is the length of the minor arc connecting the two hands?

Explanation:

Our clock looks roughly like this:

Now, between every number on the clock, there are  or  degrees. Therefore, from  to  there are  of these sectors. Therefore, there are  degrees. To find the arc length, you use the equation:

Now, we know:

We know that . Therefore, we can write our equation:

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