Chapter 8, Problem 11P

(a)

To determine

Find the amount of fuel consumed by the cars on average daily basis.

Express the answer in gallons/day and liters/day.

Answer to Problem 11P

The amount of fuel consumed on average daily basis in gallons/day is $\underset{\_}{2.47\times {10}^8\text{gallons/day}}$.

The amount of fuel consumed on average daily basis in liters/day is $\underset{\_}{9.36\times {10}^8\text{liters/day}}$.

Explanation of Solution

Given information:

The average distance travelled by the car is 12,000 miles per year.

The gas consumption rate of the car is 20 miles/gallon.

The sample size is 150 million cars.

Calculation:

Find the amount of fuel consumed on average daily basis using the relation.

$\begin{array}{c}\left\{\begin{array}{l}\text{Amount}\text{of}\text{fuel}\text{consumed}\\ \text{on}\text{average daily}\text{basis}\end{array}\right\}=\frac{\text{Average}\text{distance}\times \text{Number}\text{of}\text{cars}}{\text{Gas}\text{consumption}\text{rate}}\\ =\frac{12,000\frac{\text{miles}}{\text{year}}\times \frac{\text{1}\text{year}}{\text{365}\text{days}}\times 150\times {10}^6}{20\frac{\text{miles}}{\text{gallon}}}\\ =2.47\times {10}^8\text{gallons/day}\end{array}$

Therefore, the amount of fuel consumed on average daily basis as $\underset{\_}{2.47\times {10}^8\text{gallons/day}}$.

Convert the units from gallons/day to liters/day.

$\begin{array}{c}\text{Amount}\text{of}\text{fuel}\text{consumed}=2.47\times {10}^8\text{gallons/day}\times \frac{\text{3}\text{.79}\text{liters}}{\text{1}\text{gallons}}\\ =9.36\times {10}^8\text{liters/day}\end{array}$

Therefore, the amount of fuel consumed on average daily basis as $\underset{\_}{9.36\times {10}^8\text{liters/day}}$.

(b)

To determine

Find the amount of fuel consumed by the cars on average weekly basis.

Express the answer in gallons/week and liters/week.

Answer to Problem 11P

The amount of fuel consumed on average weekly basis in gallons/week is $\underset{\_}{1.73\times {10}^9\text{gallons/week}}$.

The amount of fuel consumed on average weekly basis in liters/week is $\underset{\_}{6.56\times {10}^9\text{liters/week}}$.

Explanation of Solution

Given information:

The average distance travelled by the car is 12,000 miles per year.

The gas consumption rate of the car is 20 miles/gallon.

The sample size is 150 million cars.

Calculation:

Find the amount of fuel consumed on average weekly basis using the relation.

$\begin{array}{c}\left\{\begin{array}{l}\text{Amount}\text{of}\text{fuel}\text{consumed}\\ \text{ on average weekly basis}\end{array}\right\}=\frac{\text{Average}\text{distance}\times \text{Number}\text{of}\text{cars}}{\text{Gas}\text{consumption}\text{rate}}\\ =\frac{12,000\frac{\text{miles}}{\text{year}}\times \frac{\text{1}\text{year}}{\text{52}\text{weeks}}\times 150\times {10}^6}{20\frac{\text{miles}}{\text{gallon}}}\\ =1.73\times {10}^9\text{gallons/week}\end{array}$

Therefore, the amount of fuel consumed on average weekly basis as $\underset{\_}{1.73\times {10}^9\text{gallons/week}}$.

Convert the units from gallons/weekly to liters/weekly.

$\begin{array}{c}\text{Amount}\text{of}\text{fuel}\text{consumed}=1.73\times {10}^9\text{gallons/week}\times \frac{\text{3}\text{.79}\text{liters}}{\text{1}\text{gallons}}\\ =6.56\times {10}^9\text{liters/week}\end{array}$

Therefore, the amount of fuel consumed on average weekly basis as $\underset{\_}{6.56\times {10}^9\text{liters/week}}$.

(c)

To determine

Find the amount of fuel consumed by the cars on average monthly basis.

Express the answer in gallons/month and liters/month.

Answer to Problem 11P

Therefore, the amount of fuel consumed on average monthly basis in gallons/month is $\underset{\_}{7.5\times {10}^9\text{gallons/month}}$.

Therefore, the amount of fuel consumed on average monthly basis in liters/month is $\underset{\_}{28.43\times {10}^9\text{liters/month}}$.

Explanation of Solution

Given information:

The average distance travelled by the car is 12,000 miles per year.

The gas consumption rate of the car is 20 miles/gallon.

The sample size is 150 million cars.

Calculation:

Find the amount of fuel consumed on average monthly basis using the relation.

$\begin{array}{c}\left\{\begin{array}{l}\text{Amount}\text{of}\text{fuel}\text{consumed }\\ \text{on average monthly basis}\end{array}\right\}=\frac{\text{Average}\text{distance}\times \text{Number}\text{of}\text{cars}}{\text{Gas}\text{consumption}\text{rate}}\\ =\frac{12,000\frac{\text{miles}}{\text{year}}\times \frac{\text{1}\text{year}}{\text{12}\text{months}}\times 150\times {10}^6}{20\frac{\text{miles}}{\text{gallon}}}\\ =7.5\times {10}^9\text{gallons/month}\end{array}$

Therefore, the amount of fuel consumed on average monthly basis as $\underset{\_}{7.5\times {10}^9\text{gallons/month}}$.

Convert the units from gallons/month to liters/month.

$\begin{array}{c}\text{Amount}\text{of}\text{fuel}\text{consumed}=7.5\times {10}^9\text{gallons/month}\times \frac{\text{3}\text{.79}\text{liters}}{\text{1}\text{gallons}}\\ =28.43\times {10}^9\text{liters/month}\end{array}$

Therefore, the amount of fuel consumed on average monthly basis as $\underset{\_}{28.43\times {10}^9\text{liters/month}}$.

(d)

To determine

Find the amount of fuel consumed by the cars on average yearly basis.

Express the answer in gallons/year and liters/year.

Answer to Problem 11P

The amount of fuel consumed on average yearly basis in gallons/year as $\underset{\_}{9\times {10}^{10}\text{gallons/year}}$.

The amount of fuel consumed on average yearly basis in liters/year as $\underset{\_}{34.11\times {10}^{10}\text{liters/year}}$.

Explanation of Solution

Given information:

The average distance travelled by the car is 12,000 miles per year.

The gas consumption rate of the car is 20 miles/gallon.

The sample size is 150 million cars.

Calculation:

Find the amount of fuel consumed on average yearly basis using the relation.

$\begin{array}{c}\left\{\begin{array}{l}\text{Amount}\text{of}\text{fuel}\text{consumed }\\ \text{on average yearly basis}\end{array}\right\}=\frac{\text{Average}\text{distance}\times \text{Number}\text{of}\text{cars}}{\text{Gas}\text{consumption}\text{rate}}\\ =\frac{12,000\frac{\text{miles}}{\text{year}}\times 150\times {10}^6}{20\frac{\text{miles}}{\text{gallon}}}\\ =9\times {10}^{10}\text{gallons/year}\end{array}$

Therefore, the amount of fuel consumed on average yearly basis as $\underset{\_}{9\times {10}^{10}\text{gallons/year}}$.

Convert the units from gallons/year to liters/year.

$\begin{array}{c}\text{Amount}\text{of}\text{fuel}\text{consumed}=9\times {10}^{10}\text{gallons/year}\times \frac{\text{3}\text{.79}\text{liters}}{\text{1}\text{gallons}}\\ =34.11\times {10}^{10}\text{liters/year}\end{array}$

Therefore, the amount of fuel consumed on average yearly basis as $\underset{\_}{34.11\times {10}^{10}\text{liters/year}}$

(e)

To determine

Find the amount of fuel consumed by the cars over a period of 10 years.

Express the answer in gallons and liters.

Answer to Problem 11P

The amount of fuel consumed over a period of 10 years in gallons is $\underset{\_}{9\times {10}^{11}\text{gallons}}$.

The amount of fuel consumed over a period of 10 years in liters is $\underset{\_}{34.11\times {10}^{11}\text{liters}}$.

Explanation of Solution

Given information:

The average distance travelled by the car is 12,000 miles per year.

The gas consumption rate of the car is 20 miles/gallon.

The sample size is 150 million cars.

Calculation:

Find the amount of fuel consumed over a period of 10 years basis using the relation.

$\begin{array}{c}\left\{\begin{array}{l}\text{Amount}\text{of}\text{fuel}\text{consumed }\\ \text{over a period of 10 years}\end{array}\right\}=\frac{\text{Average}\text{distance}\times \text{Number}\text{of}\text{years}\times \text{Number}\text{of}\text{cars}}{\text{Gas}\text{consumption}\text{rate}}\\ =\frac{12,000\frac{\text{miles}}{\text{year}}\times 10\text{years}\times 150\times {10}^6}{20\frac{\text{miles}}{\text{gallon}}}\\ =9\times {10}^{11}\text{gallons}\end{array}$

Therefore, the amount of fuel consumed over a period of 10 years as $\underset{\_}{9\times {10}^{11}\text{gallons}}$.

Convert the units from gallons to liters.

$\begin{array}{c}\text{Amount}\text{of}\text{fuel}\text{consumed}=9\times {10}^{11}\text{gallons}\times \frac{\text{3}\text{.79}\text{liters}}{\text{1}\text{gallons}}\\ =34.11\times {10}^{11}\text{liters}\end{array}$

Therefore, the amount of fuel consumed over a period of 10 years as $\underset{\_}{34.11\times {10}^{11}\text{liters}}$.