Chapter 1, Problem 60P

To determine

(a)

The speed that needs to be chosen for cost-effective journey.

Answer to Problem 60P

The speed that needs to be chosen for cost-effective journey is 70mph.

Explanation of Solution

Given information:

• Mileage at 60 mph − 24mpg
• Mileage at 70 mph − 20mpg
• Distance trip − 500 miles
• Gas cost - $3 per gallon
• Time worth - $18 per hour

We will have to find the best alternative which will have very loss cost bearing. The cost from both the speed alternatives shall be evaluated.

Calculation

• 60mph

At Mileage 60mph, the number of gallons (NoG) will be:

$\text{NoG=}\frac{\text{Miles}}{\text{Mileage}}$

wherein: Miles − Distance to be covered | Mileage − The distance covered in one gallon

$NoG=\frac{500}{24}=20.83$

So, 20.83 gallons required, and the cost of these gallons (CoG) at the price (P) at $3 will be:

$\begin{array}{l}CoG=NoG\times P\\ CoG=20.83\times 3\\ CoG=\$62.49\end{array}$

Now, we find the time required for driving 500 miles at 60mph

$\text{T=}\frac{\text{Miles}}{\text{Speed}}$

wherein: Miles − Distance to be covered | Speed − Speed for driving the car

$T=\frac{500}{60}=8.33$

So, 8.33 hours will be required to cover the 500-miles distance, the cost of time (CoT), with the Price (P) being 18 per hour

$\begin{array}{l}CoT=T\times P\\ CoT=8.33\times 18\\ CoT=\$149.94\end{array}$

Therefore, the total cost of the journey(CoJ) at 60 mph will be:

$\begin{array}{l}CoJ=CoG+CoT\\ CoJ=62.49+149.94\\ CoJ=\$212.43\end{array}$

• 70mph

At Mileage 70mph, the number of gallons (NoG) will be:

$\text{NoG=}\frac{\text{Miles}}{\text{Mileage}}$

wherein: Miles − Distance to be covered | Mileage − The distance covered in one gallon

$NoG=\frac{500}{20}=25$

So, 25 gallons required, and the cost of these gallons (CoG) at the price (P) at $3 will be:

$\begin{array}{l}CoG=NoG\times P\\ CoG=25\times 3\\ CoG=\$75\end{array}$

Now, we find the time required for driving 500 miles at 70mph

$\text{T=}\frac{\text{Miles}}{\text{Speed}}$

wherein: Miles − Distance to be covered | Speed − Speed for driving the car

$T=\frac{500}{70}=7.14$

So, 8.33 hours will be required to cover the 500-miles distance, the cost of time(CoT), with the Price (P) being 18 per hour

$\begin{array}{l}CoT=T\times P\\ CoT=7.14\times 18\\ CoT=\$128.52\end{array}$

Therefore, the total cost of the journey(CoJ) at 70 mph will be:

$\begin{array}{l}CoJ=CoG+CoT\\ CoJ=75+128.52\\ CoJ=\$203.52\end{array}$.

Conclusion:

The Cost of Journey at 60mph is $212.43 and 70 mph is $203.52. Therefore, 70mph should be chosen.

To determine

(b)

The speed that needs to be chosen for cost-effective journey.

Answer to Problem 60P

The speed that needs to be chosen for cost-effective journey is 60mph.

Explanation of Solution

Given information:

• Mileage at 60 mph − 24mpg
• Mileage at 70 mph − 20mpg
• Distance trip − 500 miles
• Gas cost - $4 per gallon
• Time worth - $12 per hour

We will have to find the best alternative which will have very loss cost bearing. The cost from both the speed alternatives shall be evaluated.

Calculation

• 60mph

At Mileage 60mph, the number of gallons (NoG) will be:

$\text{NoG=}\frac{\text{Miles}}{\text{Mileage}}$

wherein: Miles − Distance to be covered | Mileage − The distance covered in one gallon

$NoG=\frac{500}{24}=20.83$

So, 20.83 gallons required, and the cost of these gallons (CoG) at the price (P) at $4 will be:

$\begin{array}{l}CoG=NoG\times P\\ CoG=20.83\times 4\\ CoG=\$83.32\end{array}$

Now, we find the time required for driving 500 miles at 60mph

$\text{T=}\frac{\text{Miles}}{\text{Speed}}$

wherein: Miles − Distance to be covered | Speed − Speed for driving the car

$T=\frac{500}{60}=8.33$

So, 8.33 hours will be required to cover the 500-miles distance, the cost of time(CoT), with the Price (P) being 12 per hour

$\begin{array}{l}CoT=T\times P\\ CoT=8.33\times 12\\ CoT=\$99.96\end{array}$

Therefore, the total cost of the journey(CoJ) at 60 mph will be:

$\begin{array}{l}CoJ=CoG+CoT\\ CoJ=83.32+99.96\\ CoJ=\$183.28\end{array}$

• 70mph

At Mileage 70mph, the number of gallons (NoG) will be:

$\text{NoG=}\frac{\text{Miles}}{\text{Mileage}}$

wherein: Miles − Distance to be covered | Mileage − The distance covered in one gallon

$NoG=\frac{500}{20}=25$

So, 25 gallons required, and the cost of these gallons (CoG) at the price (P) at $4 will be:

$\begin{array}{l}CoG=NoG\times P\\ CoG=25\times 4\\ CoG=\$100\end{array}$

Now, we find the time required for driving 500 miles at 70mph

$\text{T=}\frac{\text{Miles}}{\text{Speed}}$

wherein: Miles − Distance to be covered | Speed − Speed for driving the car

$T=\frac{500}{70}=7.14$

So, 8.33 hours will be required to cover the 500-miles distance, the cost of time(CoT), with the Price (P) being 12 per hour

$\begin{array}{l}CoT=T\times P\\ CoT=7.14\times 12\\ CoT=\$85.68\end{array}$

Therefore, the total cost of the journey(CoJ) at 70 mph will be:

$\begin{array}{l}CoJ=CoG+CoT\\ CoJ=100+85.68\\ CoJ=\$185.68\end{array}$.

Conclusion:

The Cost of Journey at 60mph is $183.28and 70 mph is $185.68. Therefore, 60mph should be chosen.

To determine

(c)

The speed that needs to be chosen for cost-effective journey.

Answer to Problem 60P

The speed that needs to be chosen for cost-effective journey is 60mph.

Explanation of Solution

Given information:

• Mileage at 60 mph − 24mpg
• Mileage at 70 mph − 20mpg
• Distance trip − 500 miles
• Gas cost - $5 per gallon
• Time worth - $9 per hour

We will have to find the best alternative which will have very loss cost bearing. The cost from both the speed alternatives shall be evaluated.

Calculation

• 60mph

At Mileage 60mph, the number of gallons (NoG) will be:

$\text{NoG=}\frac{\text{Miles}}{\text{Mileage}}$

wherein: Miles − Distance to be covered | Mileage − The distance covered in one gallon

$NoG=\frac{500}{24}=20.83$

So, 20.83 gallons required, and the cost of these gallons (CoG) at the price (P) at $5 will be:

$\begin{array}{l}CoG=NoG\times P\\ CoG=20.83\times 5\\ CoG=\$104.15\end{array}$

Now, we find the time required for driving 500 miles at 60mph

$\text{T=}\frac{\text{Miles}}{\text{Speed}}$

wherein: Miles − Distance to be covered | Speed − Speed for driving the car

$T=\frac{500}{60}=8.33$

So, 8.33 hours will be required to cover the 500-miles distance, the cost of time(CoT), with the Price (P) being 9 per hour

$\begin{array}{l}CoT=T\times P\\ CoT=8.33\times 9\\ CoT=\$74.97\end{array}$

Therefore, the total cost of the journey(CoJ) at 60 mph will be:

$\begin{array}{l}CoJ=CoG+CoT\\ CoJ=104.15+74.97\\ CoJ=\$179.12\end{array}$

• 70mph

At Mileage 70mph, the number of gallons (NoG) will be:

$\text{NoG=}\frac{\text{Miles}}{\text{Mileage}}$

wherein: Miles − Distance to be covered | Mileage − The distance covered in one gallon

$NoG=\frac{500}{20}=25$

So, 25 gallons required, and the cost of these gallons (CoG) at the price (P) at $5 will be:

$\begin{array}{l}CoG=NoG\times P\\ CoG=25\times 5\\ CoG=\$125\end{array}$

Now, we find the time required for driving 500 miles at 70mph

$\text{T=}\frac{\text{Miles}}{\text{Speed}}$

wherein: Miles − Distance to be covered | Speed − Speed for driving the car

$T=\frac{500}{70}=7.14$

So, 8.33 hours will be required to cover the 500-miles distance, the cost of time(CoT), with the Price (P) being 9 per hour

$\begin{array}{l}CoT=T\times P\\ CoT=7.14\times 9\\ CoT=\$64.26\end{array}$

Therefore, the total cost of the journey(CoJ) at 70 mph will be:

$\begin{array}{l}CoJ=CoG+CoT\\ CoJ=125+64.26\\ CoJ=\$189.26\end{array}$.

Conclusion:

The Cost of Journey at 60mph is $179.12and 70 mph is $189.26. Therefore, 60mph should be chosen.

To determine

(d)

The speed that needs to be chosen for cost-effective journey.

Answer to Problem 60P

Build in the spreadsheet.

Explanation of Solution

Given information:

• Mileage at 60 mph − 24 mpg
• Mileage at 70 mph − 20 mpg
• Distance trip − 500 miles

• We will have to find the best alternative which will have very loss cost bearing. The cost from both the speed alternatives shall be evaluated.

Calculation:

• 60 mph

Distance to be covered	Speed	Mileage	NoG	Price	CoG	Time	Price	CoT	CoJ
500	60	24	20.83	2	41.67	8.33	6	50.00	91.67
500	60	24	20.83	3	62.50	8.33	6	50.00	112.50
500	60	24	20.83	4	83.33	8.33	6	50.00	133.33
500	60	24	20.83	5	104.17	8.33	6	50.00	154.17
500	60	24	20.83	2	41.67	8.33	9	75.00	116.67
500	60	24	20.83	3	62.50	8.33	9	75.00	137.50
500	60	24	20.83	4	83.33	8.33	9	75.00	158.33
500	60	24	20.83	5	104.17	8.33	9	75.00	179.17
500	60	24	20.83	2	41.67	8.33	12	100.00	141.67
500	60	24	20.83	3	62.50	8.33	12	100.00	162.50
500	60	24	20.83	4	83.33	8.33	12	100.00	183.33
500	60	24	20.83	5	104.17	8.33	12	100.00	204.17
500	60	24	20.83	2	41.67	8.33	15	125.00	166.67
500	60	24	20.83	3	62.50	8.33	15	125.00	187.50
500	60	24	20.83	4	83.33	8.33	15	125.00	208.33
500	60	24	20.83	5	104.17	8.33	15	125.00	229.17
500	60	24	20.83	2	41.67	8.33	18	150.00	191.67
500	60	24	20.83	3	62.50	8.33	18	150.00	212.50
500	60	24	20.83	4	83.33	8.33	18	150.00	233.33
500	60	24	20.83	5	104.17	8.33	18	150.00	254.17

• 70 mph

Distance to be covered	Speed	Mileage	NoG	Price	CoG	Time	Price	CoT	CoJ
500	70	20	20.83	2	41.67	7.14	6	42.86	84.52
500	70	20	20.83	3	62.50	7.14	6	42.86	105.36
500	70	20	20.83	4	83.33	7.14	6	42.86	126.19
500	70	20	20.83	5	104.17	7.14	6	42.86	147.02
500	70	20	20.83	2	41.67	7.14	9	64.29	105.95
500	70	20	20.83	3	62.50	7.14	9	64.29	126.79
500	70	20	20.83	4	83.33	7.14	9	64.29	147.62
500	70	20	20.83	5	104.17	7.14	9	64.29	168.45
500	70	20	20.83	2	41.67	7.14	12	85.71	127.38
500	70	20	20.83	3	62.50	7.14	12	85.71	148.21
500	70	20	20.83	4	83.33	7.14	12	85.71	169.05
500	70	20	20.83	5	104.17	7.14	12	85.71	189.88
500	70	20	20.83	2	41.67	7.14	15	107.14	148.81
500	70	20	20.83	3	62.50	7.14	15	107.14	169.64
500	70	20	20.83	4	83.33	7.14	15	107.14	190.48
500	70	20	20.83	5	104.17	7.14	15	107.14	211.31
500	70	20	20.83	2	41.67	7.14	18	128.57	170.24
500	70	20	20.83	3	62.50	7.14	18	128.57	191.07
500	70	20	20.83	4	83.33	7.14	18	128.57	211.90
500	70	20	20.83	5	104.17	7.14	18	128.57	232.74