Question

homework 2.8 hw - extending unit analysis
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the energy efficiency of electric vehicles is usually stated 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 150 miles?
c. if you drive 12,000 miles in a year, what is the cost of a years worth of travel in this electric car?
d. if you drive a gas - powered car with mileage of 31 mpg (miles per gallon) and paid $2.40/gal, how much would it cost to drive 12,000 miles?
a. driving 150 miles requires \\(\boxed{}\\) kwh of energy

Explanation:

Step 1: Identify the rate

The electric car's energy efficiency is given as \( 24 \, \text{kWh/100 mi} \). This means for every 100 miles, the car uses 24 kilowatt - hours of energy.

Step 2: Set up the proportion

We want to find the energy \( E \) (in kWh) required to drive 150 miles. We can set up a proportion: \( \frac{24 \, \text{kWh}}{100 \, \text{mi}}=\frac{E}{150 \, \text{mi}} \)

Step 3: Solve for \( E \)

Cross - multiply to get \( 100E = 24\times150 \). Then \( E=\frac{24\times150}{100} \). First, calculate \( 24\times150 = 3600 \), then divide by 100: \( E = 36 \)

Answer:

36