GRE Math : How to find the distance between clock hands

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Example Question #2 : 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?

Possible Answers:

$4.5\pi\:in$

$7\pi\:in$

$\frac{10\pi}{3}\:in$

$\frac{3\pi}{7}\:in$

$6\pi\:in$

Correct answer:

$\frac{10\pi}{3}\:in$

Explanation:

Our clock looks roughly like this:

Clock124

Now, between every number on the clock, there are $\frac{360}{12}$ or degrees. Therefore, from to , there are 4*30=120 degrees. To find the arc length, you use the equation:

$\frac{degrees}{360}*Circumference$

Now, we know:

$C=2\pi r$

We know that r=5 . Therefore, we can write our equation:

$\frac{120}{360}*2*\pi*5=\frac{1}{3}*10\pi=\frac{10\pi}{3}$

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Example Question #1 : 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?

Possible Answers:

$\frac{3\pi}{2}$

$12\pi$

$\frac{7\pi}{3}$

$\frac{9\pi}{2}$

$2\pi$

Correct answer:

$\frac{9\pi}{2}$

Explanation:

Our clock looks roughly like this:

Clock3

Now, between every number on the clock, there are $\frac{360}{12}$ 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 9*15=135 degrees. To find the arc length, you use the equation:

$\frac{degrees}{360}*Circumference$

Now, we know:

$C=2\pi r$

We know that r=6 . Therefore, we can write our equation:

$\frac{135}{360}*2*\pi*6=\frac{3}{8}*12\pi=\frac{9\pi}{2}$

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Example Question #3 : 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?

Possible Answers:

$\pi$

$2\pi$

$\frac{2\pi}{5}$

$1.25\pi$

$\frac{\pi}{6}$

Correct answer:

$\pi$

Explanation:

Our clock looks roughly like this:

Clock1210

Now, between every number on the clock, there are $\frac{360}{12}$ or degrees. Therefore, from to there are of these sectors. Therefore, there are 2*30=60 degrees. To find the arc length, you use the equation:

$\frac{degrees}{360}*Circumference$

Now, we know:

$C=2\pi r$

We know that r=3 . Therefore, we can write our equation:

$\frac{60}{360}*2*\pi*3=\frac{1}{6}*6\pi=\pi$

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GRE Math : How to find the distance between clock hands

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Example Questions

Example Question #2 : How To Find The Distance Between Clock Hands

Example Question #1 : How To Find The Distance Between Clock Hands

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

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