1. How many miles over the lifetime of the car would you have to drive in order for it to make sense to purchase the Tesla over the Prius? 2. How much money would you spend (on car purchase and gas/electricity only) for the cost of the Tesla and Honda Civic to be the same? Round your answer to the nearest dollar amount. 3. Josh is planning on driving his new car for at least 250,000 miles. Which car (Honda Civic, Toyota Prius, or Tesla) would be his best option based on sale price and cost per mile? Explain your answer.

1 answer

To answer your questions, I will need some typical data for the Mitsubishi Mirage, Toyota Prius, and Tesla, including purchase prices, fuel efficiencies, maintenance costs, and electricity costs. Here's a general assumption based on commonly known facts.

  1. Cost Comparison Between Tesla and Prius:

    • Purchase Price:

      • Tesla Model 3: Approx. $40,000
      • Toyota Prius: Approx. $25,000
    • Fuel Efficiency:

      • Prius: Approx. 50 miles per gallon (MPG)
      • Tesla: Electric, with energy consumption typically calculated around 4 miles per kWh, which will vary based on charging costs.
    • Gas Prices:

      • Assume $4.00 per gallon.
    • Electricity Costs:

      • Assume $0.13 per kWh.
    • Lifecycle Cost Calculation: For the Prius: \[ \text{Cost of Gas per mile} = \frac{4.00}{50} = 0.08 \text{ (cents per mile)} \] For the Tesla: \[ \text{Cost of Electricity per mile} = \frac{0.13}{4} = 0.0325 \text{ (cents per mile)} \]

    To find the break-even point (where the total costs equalize), we'll set up the equation: \[ 25,000 + 0.08m = 40,000 + 0.0325m \] Solving for \( m \): \[ 25,000 + 0.08m - 0.0325m = 40,000 \] \[ 25,000 - 40,000 = 0.08m - 0.0325m \] \[ -15,000 = 0.0475m \] \[ m \approx \frac{15,000}{0.0475} \approx 315,789 \text{ miles} \]

    Thus, you would have to drive roughly 315,789 miles over the lifetime of the car for it to make sense to purchase the Tesla over the Prius.

  2. Equal Cost Calculation Between Tesla and Honda Civic:

    • Purchasing Costs:

      • Tesla Model 3: Approx. $40,000
      • Honda Civic: Approx. $22,000
    • Civic Mileage:

      • Assume 30 MPG: \[ \text{Civic:} \quad \text{Cost of Gas per mile} = \frac{4.00}{30} \approx 0.1333 \text{ (cents per mile)} \]

    Let \( m \) be the number of miles driven for the total cost to be equal: \[ 22,000 + 0.1333m = 40,000 + 0.0325m \] Rearranging gives: \[ 22,000 - 40,000 = 0.0325m - 0.1333m \] \[ -18,000 = -0.1008m \] \[ m \approx \frac{18,000}{0.1008} \approx 178,571 \text{ miles} \]

    Hence, you would need to drive approximately 178,571 miles for the costs of the Tesla and Honda Civic to be the same.

  3. Best Option for Josh Driving 250,000 Miles:

    Using the earlier calculations of cost per mile:

    • Honda Civic: Cost per mile = $0.1333 \[ \text{Total cost for 250,000 miles} = 22,000 + (0.1333 \times 250,000) = 22,000 + 33,325 = 55,325 \]
    • Toyota Prius: Cost per mile = $0.08 \[ \text{Total cost for 250,000 miles} = 25,000 + (0.08 \times 250,000) = 25,000 + 20,000 = 45,000 \]
    • Tesla: Cost per mile = $0.0325 \[ \text{Total cost for 250,000 miles} = 40,000 + (0.0325 \times 250,000) = 40,000 + 8,125 = 48,125 \]

    Comparing the total costs:

    • Honda Civic: $55,325
    • Toyota Prius: $45,000
    • Tesla: $48,125

    Josh’s best option based on total lifetime cost is the Toyota Prius as it has the lowest total cost at $45,000.