Question

A snail can move 1/30 miles in 1/3 hour. How fast does a snail move in miles /hours

Answer 1

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.

Unit Rate

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.

Proportions

Proportions look like two fractions set equal to each other with a missing variable to solve.

State our variables

let x be the number of miles per hour

Write a proportion

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, x, that we are solving for. We can write x in the numerator.

$\displaystyle{\frac{\frac{1}{30}\ mi}{\frac{1}{3}\ hr} = \frac{x\ mi}{1\ hr}}$

Solve

We can solve by finding the scale factor. The scale factor is the number we can multiply the numerator by to find x.

Find the scale factor

Start with the proportion.

$\displaystyle{\frac{\frac{1}{30}\ mi}{\frac{1}{3}\ hr} = \frac{x\ mi}{1\ hr}}$

To find the scale factor,

1. Take the denominator from the fraction with a variable: $1\ hr$
2. Take the denominator from the fraction that has no variable:  $\frac{1}{3}\ hr$
3. Divide step 1 by step 2 and solve:  $1\ hr\ \div\ \frac{1}{3}\ hr = 3$

Our scale factor is 3.

Solve for x

We can find x by multiplying the numerator in the first fraction by the scale factor. This is because x is also in the numerator.

$\displaystyle{\frac{\frac{1}{30}\ mi}{\frac{1}{3}\ hr} = \frac{(\frac{1}{30}\ mi)*3}{1\ hr}}$

$\displaystyle{\frac{\frac{1}{30}\ mi}{\frac{1}{3}\ hr} = \frac{\frac{3}{30}\ mi}{1\ hr}}$

Simplify 3/30 by dividing the fraction by 3.

$\displaystyle{\frac{\frac{1}{30}\ mi}{\frac{1}{3}\ hr} = \frac{\frac{1}{10}\ mi}{1\ hr}}$

x = 1/10

∴ a snail moves 1/10 miles per hour.

Learn another way to solve proportions here: brainly.com/question/18437927