Question

the energy efficiency of electric vehicles is usually rated in terms of the kilowatt hours (of energy) required to drive 100 miles, or kwh/100 mi. an electric car is rated at 24 kwh/100 mi

a. how much energy (in kilowatt hours) is required to drive this electric car 150 miles?
b. assuming electricity costs $0.12/kwh, how much does it cost to drive this electric car 60 miles?
c. if you drive 12,000 miles in a year, what is the cost of a year’s worth of travel in this electric car?
d. if you drove a gas - powered car with mileage of 31 mpgal and paid $2.40/gal, how much would it cost to drive 12,000 miles?

a. driving 150 miles requires 36 kwh of energy

b. it costs $0.864? to drive 60 miles
(found to the nearest cent as needed.)

Explanation:

Part a

Step1: Understand the rate

The car is rated at \(24\) kWh/100 mi, meaning for every 100 miles, it uses 24 kWh.

Step2: Set up the proportion

Let \(x\) be the energy for 150 miles. We have \(\frac{24\ \text{kWh}}{100\ \text{mi}}=\frac{x}{150\ \text{mi}}\).

Step3: Solve for \(x\)

Cross - multiply: \(100x = 24\times150\). Then \(x=\frac{24\times150}{100}=24\times1.5 = 36\) kWh.

Step1: Find energy for 60 miles

First, use the rate \(\frac{24\ \text{kWh}}{100\ \text{mi}}\). Let \(y\) be the energy for 60 miles. \(\frac{24}{100}=\frac{y}{60}\), so \(y=\frac{24\times60}{100}=14.4\) kWh.

Step2: Calculate cost

Electricity costs \(\$0.12\) per kWh. Cost \(=14.4\times0.12=\$1.728\approx\$1.73\) (rounded to the nearest cent).

Step1: Find energy for 12000 miles

Using the rate \(\frac{24\ \text{kWh}}{100\ \text{mi}}\), let \(z\) be the energy for 12000 miles. \(\frac{24}{100}=\frac{z}{12000}\), so \(z=\frac{24\times12000}{100}=24\times120 = 2880\) kWh.

Step2: Calculate cost

Cost \(=2880\times0.12=\$345.60\).

Answer:

36 kWh

Part b