Chapter 1, Problem 60P

(a)

To determine

The speed at which the 525 miles trip will be completed.

Answer to Problem 60P

The cost is lower at 70 mph as compared to 60 mph, hence speed should be 70 miles per hour.

Explanation of Solution

To determine the optimum level of speed at which 525miles trip will be done, we need to compare the total cost to be incurred at both the speed levels.

At 60 mph

  $\begin{array}{l}\hfill \\ \text{If 1 gallon gives 29 miles per hour, then 525 miles will require:}\hfill \\ \begin{array}{l}=\frac{525}{29}\\ =18.1\text{ gallons of gas}\end{array}\hfill \\ \text{If 60 miles is covered in 1 hour, then 525 miles will take:}\hfill \\ \begin{array}{l}=\frac{525}{60}\\ =8.75\text{ hours}\end{array}\hfill \end{array}$

At 70 mph

  $\begin{array}{l}\text{If }1\text{ gallon gives }25\text{ miles per hour, then }525\text{ miles will require:}\hfill \\ \begin{array}{l}=\frac{525}{25}\\ =21\text{ gallons of gas}\end{array}\hfill \\ \text{If }70\text{ miles is covered in }1\text{ hour, then }525\text{ miles will take:}\hfill \\ \begin{array}{l}=\frac{525}{70}\\ =7.5\text{ hours}\end{array}\hfill \end{array}$

Calculation of cost:

If gas has $3 cost and time is $18 per hour:

At 60 mph speed:

  $\begin{array}{l}\begin{array}{c}\text{Cost of gas}=3\times 18.1\\ =\$54.3\end{array}\hfill \\ \begin{array}{c}\text{Cost of time}=18\times 8.75\\ =\$157.5\end{array}\hfill \\ \begin{array}{c}\text{Hence, total cost}=\$54.3+\$157.5\\ =\$211.8\end{array}\hfill \end{array}$

At 70 mph speed:

  $\begin{array}{l}\begin{array}{c}\text{Cost of gas}=3\times 21\\ =\$63\end{array}\hfill \\ \begin{array}{c}\text{Cost of time}=18\times 7.5\\ =\$135\end{array}\hfill \\ \begin{array}{c}\text{Hence, total cost}=\$63+\$135\\ =\$198\end{array}\hfill \end{array}$

Since cost is lower at 70 miles per hour, speed should be 70 miles per hour.

(b)

To determine

The speed at which the 525miles trip will be completed.

Answer to Problem 60P

The cost is lower at 70 mph as compared to 60 mph, hence speed should be 70 miles per hour.

Explanation of Solution

To determine the optimum level of speed at which 525 miles trip will be done, we need to compare the total cost to be incurred at both the speed levels.

Calculation of cost:

If gas has $4 cost and time is $12 per hour:

At 60 mph speed:

  $\begin{array}{l}\begin{array}{c}\text{Cost of gas}=4\times 18.1\\ =\$72.41\end{array}\hfill \\ \begin{array}{c}\text{Cost of time}=12\times 8.75\\ =\$105\end{array}\hfill \\ \begin{array}{c}\text{Hence, total cost}=\$72.4+\$105\\ =\$177.41\end{array}\hfill \end{array}$

At 70 mph speed:

  $\begin{array}{l}\begin{array}{c}\text{Cost of gas}=4\times 21\\ =\$84\end{array}\hfill \\ \begin{array}{c}\text{Cost of time}=12\times 7.5\\ =\$90\end{array}\hfill \\ \begin{array}{c}\text{Hence, total cost}=\$84+\$90\\ =\$174\end{array}\hfill \end{array}$

Since cost is lower at 70 miles per hour, speed should be 70 miles per hour.

(c)

To determine

The speed at which the 525 miles trip will be completed.

Answer to Problem 60P

The cost is lower at 60 mph as compared to 70 mph, hence speed should be 60 miles per hour.

Explanation of Solution

To determine the optimum level of speed at which 525 miles trip will be done, we need to compare the total cost to be incurred at both the speed levels.

Calculation of cost:

If gas has $5 cost and time is $9 per hour:

At 60 mph speed:

  $\begin{array}{l}\begin{array}{c}\text{Cost of gas}=5\times 18.1\\ =\$90.5\end{array}\hfill \\ \begin{array}{c}\text{Cost of time}=9\times 8.75\\ =\$78.75\end{array}\hfill \\ \begin{array}{c}\text{Hence, total cost}=\$90.5+\$78.75\\ =\$169.25\end{array}\hfill \end{array}$

At 70 mph speed:

  $\begin{array}{l}\begin{array}{c}\text{Cost of gas}=5\times 21\\ =\$105\end{array}\hfill \\ \begin{array}{c}\text{Cost of time}=9\times 7.5\\ =\$67.5\end{array}\hfill \\ \begin{array}{c}\text{Hence, total cost}=\$105+\$67.5\\ =\$172.5\end{array}\hfill \end{array}$

Since cost is lower at 60 miles per hour, speed should be 60 miles per hour.

(d)

To determine

To build a spreadsheet showing the calculation of total trip cost at various rates of gas costs and time cost for 60mph speed and 70mph speed.

Answer to Problem 60P

The tables reflect the total trip cost at both the speed levels of 60 mph and 70 mph considering various rates of gas cost and time costs given in the question

Explanation of Solution

At 60 mph considering 18.1 gallons and 8.75 hrs.
	2	3	4	5
6	$88.7	$106.8	$124.9	$143.0
9	$115.0	$133.1	$151.2	$169.3
12	$141.2	$159.3	$177.4	$195.5
15	$167.5	$185.6	$203.7	$221.8
18	$193.7	$211.8	$229.9	$248.0

At 70 mph considering 21 gallons and 7.5 hrs.
	2	3	4	5
6	$87.0	$108.0	$129.0	$150.0
9	$109.5	$130.5	$151.5	$172.5
12	$132.0	$153.0	$174.0	$195.0
15	$154.5	$175.5	$196.5	$217.5
18	$177.0	$198.0	$219.0	$240.0

The tables above reflect the total trip cost at both the speed levels of 60 mph and 70 mph considering various rates of gas cost and time costs given in the question.