Answer: 1/10 miles/hour
To find how fast a snail moves in miles per hour, we can find the unit rate using a proportion.
<h2>Unit Rate</h2>
The unit rate is the amount per one unit. In this problem, the unit is for one hour. One way to find the unit rate is by using a proportion.
<h2>Proportions</h2>
Proportions look like two fractions set equal to each other with a missing variable to solve.
<h3>State our variables</h3>
let <em>x</em> be the number of miles per hour
<h3>Write a proportion</h3>
The first fraction has a number for the numerator (top) and denominator (bottom), because the question gives us the information. The second fraction has a missing value, <em>x</em>, that we are solving for. We can write <em>x</em> in the numerator.
![\displaystyle{\frac{\frac{1}{30}\ mi}{\frac{1}{3}\ hr} = \frac{x\ mi}{1\ hr}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%7B%5Cfrac%7B%5Cfrac%7B1%7D%7B30%7D%5C%20mi%7D%7B%5Cfrac%7B1%7D%7B3%7D%5C%20hr%7D%20%3D%20%5Cfrac%7Bx%5C%20mi%7D%7B1%5C%20hr%7D%7D)
<h2>Solve</h2>
We can solve by finding the scale factor. The scale factor is the number we can multiply the numerator by to find <em>x</em>.
<h3>Find the scale factor</h3>
Start with the proportion.
![\displaystyle{\frac{\frac{1}{30}\ mi}{\frac{1}{3}\ hr} = \frac{x\ mi}{1\ hr}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%7B%5Cfrac%7B%5Cfrac%7B1%7D%7B30%7D%5C%20mi%7D%7B%5Cfrac%7B1%7D%7B3%7D%5C%20hr%7D%20%3D%20%5Cfrac%7Bx%5C%20mi%7D%7B1%5C%20hr%7D%7D)
To find the scale factor,
- Take the denominator from the fraction with a variable:
![1\ hr](https://tex.z-dn.net/?f=1%5C%20hr)
- Take the denominator from the fraction that has no variable:
![\frac{1}{3}\ hr](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D%5C%20hr)
- Divide step 1 by step 2 and solve:
![1\ hr\ \div\ \frac{1}{3}\ hr = 3](https://tex.z-dn.net/?f=1%5C%20hr%5C%20%5Cdiv%5C%20%5Cfrac%7B1%7D%7B3%7D%5C%20hr%20%3D%203)
Our scale factor is <u>3</u>.
<h3>Solve for x</h3>
We can find <em>x</em> by multiplying the numerator in the first fraction by the scale factor. This is because <em>x</em> is also in the numerator.
![\displaystyle{\frac{\frac{1}{30}\ mi}{\frac{1}{3}\ hr} = \frac{(\frac{1}{30}\ mi)*3}{1\ hr}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%7B%5Cfrac%7B%5Cfrac%7B1%7D%7B30%7D%5C%20mi%7D%7B%5Cfrac%7B1%7D%7B3%7D%5C%20hr%7D%20%3D%20%5Cfrac%7B%28%5Cfrac%7B1%7D%7B30%7D%5C%20mi%29%2A3%7D%7B1%5C%20hr%7D%7D)
![\displaystyle{\frac{\frac{1}{30}\ mi}{\frac{1}{3}\ hr} = \frac{\frac{3}{30}\ mi}{1\ hr}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%7B%5Cfrac%7B%5Cfrac%7B1%7D%7B30%7D%5C%20mi%7D%7B%5Cfrac%7B1%7D%7B3%7D%5C%20hr%7D%20%3D%20%5Cfrac%7B%5Cfrac%7B3%7D%7B30%7D%5C%20mi%7D%7B1%5C%20hr%7D%7D)
Simplify 3/30 by dividing the fraction by 3.
![\displaystyle{\frac{\frac{1}{30}\ mi}{\frac{1}{3}\ hr} = \frac{\frac{1}{10}\ mi}{1\ hr}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%7B%5Cfrac%7B%5Cfrac%7B1%7D%7B30%7D%5C%20mi%7D%7B%5Cfrac%7B1%7D%7B3%7D%5C%20hr%7D%20%3D%20%5Cfrac%7B%5Cfrac%7B1%7D%7B10%7D%5C%20mi%7D%7B1%5C%20hr%7D%7D)
x = 1/10
∴ a snail moves 1/10 miles per hour.
Learn another way to solve proportions here: brainly.com/question/18437927