Chapter 6.1, Problem 31E

To determine

To calculate: The equivalent rate.

Answer to Problem 31E

The equivalent rate is $900$ miles per minute.

Explanation of Solution

Given information:

The following equivalent fractions:

  $\frac{\text{300 mi}}{\text{20 sec}}=\frac{?\text{ mi}}{1\text{ min}}$

Calculation:

To find an equivalent rate, convert from miles per second to miles per minute. To do so, multiply the rate by a conversion factor. There are $60$ seconds in $1$ minute, so $\frac{60\text{ sec}}{1\text{ min}}=1$ .

  $\begin{array}{l}\frac{\text{300 mi}}{\text{20 sec}}\\ \Rightarrow \frac{\text{300 mi}}{\text{20 sec}}\times \frac{\text{60 sec}}{1\text{ min}}\text{ [Multiply rate by common conversion factor]}\\ \Rightarrow \frac{\text{300 mi}}{\underset{1}{\cancel{20}}\cancel{\text{sec}}}\times \frac{\stackrel{3}{\cancel{60}}\cancel{\text{sec}}}{1\text{ min}}\left[\text{Divide out common factor and unit}\right]\\ \Rightarrow \frac{\text{900 mi}}{1\text{ min}}\left[\text{Simplify}\right]\end{array}$

Therefore, the equivalent rate is $900$ miles per minute.