Chapter 6.1, Problem 35E

To determine

To calculate: The equivalent rate.

Answer to Problem 35E

The equivalent rate is $0.375$ hours per mile.

Explanation of Solution

Given information:

The following equivalent fractions:

  $\frac{45\text{ min}}{\text{2 mi}}=\frac{?\text{ h}}{1\text{ mi}}$

Calculation:

To find an equivalent rate, convert from minutes per mile to hours per mile. To do so, multiply the rate by a conversion factor. There are $60$ minutes in $1$ hour, so $\frac{60\text{ minutes}}{1\text{ hour}}=1$ .

  $\begin{array}{l}\frac{45\text{ min}}{\text{2 mi}}\\ \Rightarrow \frac{45\text{ min}}{\text{2 mi}}\times \frac{\text{1 h}}{\text{60 min}} \left[\text{Multiply rate by common conversion factor}\right]\\ \Rightarrow \frac{\cancel{\stackrel{3}{45}}\cancel{\text{min}}}{\text{2 mi}}\times \frac{\text{1 h}}{\cancel{\underset{4}{\text{60}}}\cancel{\text{min}}} \left[\text{Divide out common factor and unit}\right]\\ \Rightarrow \frac{3\text{ h}}{\text{8 mi}} \left[\text{Simplify}\right]\end{array}$

To find a unit rate, denominator should be $1$ .

  $\begin{array}{l}\frac{3\text{ h}÷\text{8}}{\text{8 mi}÷\text{8}} \text{[Divide numerator and denominator by }8\text{]}\\ \Rightarrow \frac{0.375\text{ h}}{1\text{ mi}} \left[\text{Simplify}\right]\end{array}$

Therefore, the equivalent rate is $0.375$ hours per mile.