Chapter 6.1, Problem 39E

a.

To determine

To calculate: The approximate number of gallons of gasoline used on the trip.

Answer to Problem 39E

The approximate number of gallons of gasoline used on the trip is $24$ .

Explanation of Solution

Given:

Two full tanks of gasoline are used on the trip.

A tank holds $12$ gallons of gasoline.

Calculation:

To calculate the total gallons of gasoline used the trip, find the total gallons of gasoline in the two tanks used in the trip. Since each tank holds $12$ gallons of gasoline, it can be written as:

  $\frac{12\text{ gallons}}{1\text{ tank}}$

To find the number of gallons of gasoline in the two tanks, multiply the numerator and denominator by $2$

  $\begin{array}{l}\frac{12\text{ gallons}\times \text{2}}{1\text{ tank}\times 2}\\ \Rightarrow \frac{24\text{ gallons}}{2\text{ tanks}}\end{array}$

Hence there are $24$ gallons of gasoline in the two tanks.

Therefore, $24$ gallons of gasoline is used on the trip.

b.

To determine

To calculate: Approximate number of miles driven on the trip.

Answer to Problem 39E

The approximate number of miles driven on the trip is $600$ .

Explanation of Solution

Given:

The car drives about $25$ miles per gallon.

Calculation:

To calculate the number of miles driven on the trip, find the number of miles the car can drive in the amount of gasoline it has. As calculated in subpart a, $24$ gallons of gasoline is used on the trip. Since the car can drive $25$ miles per gallon, it can be written as:

  $\frac{25\text{ miles}}{1\text{ gallon}}$

To find the number of miles the car can drive in $24$ gallons of gasoline, multiply numerator and denominator by $24$

  $\begin{array}{l}\frac{25\text{ miles}\times \text{24}}{1\text{ gallon}\times \text{24}}\\ \Rightarrow \frac{600\text{ miles}}{24\text{ gallons}}\end{array}$

Hence, the car can drive $600$ miles in $24$ gallons of gasoline.

Therefore, the number of miles driven in the trip $600$ .

c.

To determine

To calculate: The money spent per mile on gasoline.

Answer to Problem 39E

The cost of gasoline per mile is $\$0.18$ .

Explanation of Solution

Given:

The car drives about $25$ miles per gallon.

The cost of gasoline is $\$4.50$ per gallon.

Calculation:

To calculate the money spent per mile on gasoline, equivalent rate is used. As given, for $1$ gallon, the car travels $25$ miles. It can be expressed as:

  $\frac{1\text{ gallon}}{25\text{ miles}}$

Multiply this by cost per gallon( $\frac{\$4.50}{1\text{ gallon}}$ ) to find cost per mile.

  $\begin{array}{l}\frac{1\cancel{\text{gallon}}}{25\text{ miles}}\cdot \frac{\$4.50}{1\cancel{\text{gallon}}} \left[\text{Divide out common factors and unit}\right]\\ \Rightarrow \frac{\$4.50}{25\text{ miles}}\end{array}$

Convert this into unit rate.

  $\begin{array}{l}\Rightarrow \frac{\$4.50÷25}{25\text{ miles}÷\text{25}} \text{ [Divide numerator and denominator by 25]}\\ \Rightarrow \frac{\$0.18}{1\text{ mile}}\end{array}$

Therefore, the cost of gasoline per mile is $\$0.18$ .

d.

To determine

To calculate: Whether there is enough money to spend on gasoline for another trip.

Answer to Problem 39E

There isn’t enough money to spend on gasoline for another trip.

Explanation of Solution

Given:

There are $\$60$ to be spent on gasoline.

The trip is $350$ miles.

The amount spent per mile on gasoline is same as the first trip.

Calculation:

To determine whether there is enough money to spend on gasoline for another trip, calculate the amount of money required for the gasoline to be used for the given distance. As calculated is subpart c, the cost of gasoline per mile is $\$0.18$ , therefore it can be written as:

  $\frac{\$0.18}{1\text{ mile}}$

To calculate the cost of gasoline for $350$ miles, multiply numerator and denominator by $350$

  $\begin{array}{l}\frac{\$0.18\times 350}{1\text{ mile}\times 350}\\ \Rightarrow \frac{\$63}{350\text{ miles}}\end{array}$

Therefore, $\$63$ is required to travel $350$ miles.

Since money to be spent is only $\$60$ which is less than the money required( $\$63$ ), there is not enough money for another trip.