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Section 2.5 Cost of Driving

Worksheet 2.5.1 Cost of Driving Worksheet
A4US

Problem Situation: Cost of Driving.

Jenna’s job requires her to travel. She owns a 2006 Toyota 4Runner, but she also has the option to rent a car for her travel. In either case, her employer will reimburse her the same amount for the mileage driven using the rate set by the Internal Revenue Service. In 2015, that rate was 57.5 cents/mile. In this lesson you will explore the question of whether it would be better for Jenna to drive her own car or to rent a car.
1.
What do you need to know to calculate the cost of Jenna driving her own car?
2.
What do you need to know to calculate the cost of Jenna renting a car?
3.
Gas mileage is rated for either city driving or highway driving. Most of Jenna’s travel will take place on the highway. For her next trip she needs to drive 193 miles from home, and then return. The price of gas is $3.50/gallon. Her 4Runner gets 22 miles/gallon. If Jenna rents, she can request a small, fuel‐efficient car such as the Hyundai Elantra, which gets 40 miles/gallon.

4.

In the last lesson, you learned about Dimensional Analysis. We will be needing those techniques again in this lesson. To warm up, consider this question:
It takes me 20 minutes to walk the loop around the lake near work. I normally walk 3 miles per hour. How many miles will I travel if I walk around the lake 4 times?
Which of the following is the correct setup to answer this question using dimensional analysis?

  1. \begin{equation*} \frac{1}{4\text{ loops around lake}} \cdot \frac{1 \text{ loop around lake}}{20\text{ minutes}} \cdot \frac{60 \text{ minutes}}{1\text{ hour}} \cdot \frac{1\text{ hour}}{3\text{ miles}} \end{equation*}

  2. \begin{equation*} \frac{4\text{ loops around lake}}{1} \cdot \frac{1 \text{ loop around lake}}{20\text{ minutes}} \cdot \frac{60 \text{ minutes}}{1\text{ hour}} \cdot \frac{1\text{ hour}}{3\text{ miles}} \end{equation*}

  3. \begin{equation*} \frac{4\text{ loops around lake}}{1} \cdot \frac{20\text{ minutes}}{1 \text{ loop around lake}} \cdot \frac{60 \text{ minutes}}{1\text{ hour}} \cdot \frac{1\text{ hour}}{3\text{ miles}} \end{equation*}

  4. \begin{equation*} \frac{4\text{ loops around lake}}{1} \cdot \frac{20\text{ minutes}}{1 \text{ loop around lake}} \cdot \frac{1\text{ hour}}{60 \text{ minutes}} \cdot \frac{3\text{ miles}}{1\text{ hour}} \end{equation*}

Then calculate the correct answer and give it below.

5.

Using the information below, calculate Jenna’s total cost of driving a rental car for a round trip.

  • Price of gas: $3.50/gallon

  • Length of trip (one way): 193 miles

  • Gas mileage of rental car: 40 miles/gallon

  • Price of the rental car: $98.98 plus 15.3% tax (Gas is not included in the rental price. The car starts with a full tank of gas when rented and must be returned to the rental agency with a full tank)

Try the problem on your own first. If you are having trouble after 2 tries, we will break it down.

6.

Using the information below, calculate Jenna’s total cost of driving her own car for a round trip.

  • Price of gas: $3.50/gallon

  • Length of trip (one way): 193 miles

  • Gas mileage of her car: 22 miles/gallon

You'll also want to incorporate these costs (we're not including every cost we could have included). What do I do with these?

  • General maintenance (oil and fluid changes): $40 every 3,000 miles

  • Tires: Tires for Jenna’s car cost $920; they are supposed to be replaced every 50,000 miles

  • Repairs: The website Edmonds.com estimates that repairs on a three-year-old 2009 4Runner will be approximately $328 per year; this is based on driving 15,000 miles

Try the problem on your own first. If you are having trouble after 2 tries, we will break it down.
Hint.
You shouldn't include the entire $40 maintenance cost because the trip is less than 3,000 miles. Same for tires and repairs.