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 38 kwh/100 mi.

a. is a vehicle rated 27 kwh/100 mi more or less efficient than this electric car?
b. how much energy (in kilowatt-hours) is required to drive this electric car 240 miles?
c. assuming electricity costs $0.13/kwh, how much does it cost to drive this electric car 450 miles?

a. a vehicle rated 27 kwh/100 mi is less/more efficient than an electric car rated 38 kwh/100 mi.

Explanation:

Compare energy efficiency ratings

Using the Dimensional Analysis knowledge point

$$ 27\text{ kWh/100 mi} < 38\text{ kWh/100 mi} $$

Since a lower rating means less energy is consumed to travel the same distance, the vehicle requiring \(27\text{ kWh}\) is more efficient.

Calculate energy for 240 miles

Using the Unit Conversion and Dimensional Analysis knowledge points

$$ E = 240\text{ mi} \times \frac{38\text{ kWh}}{100\text{ mi}} = 2.4 \times 38\text{ kWh} = 91.2\text{ kWh} $$

Calculate cost for 450 miles

Using the Unit Conversion and Dimensional Analysis knowledge points

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Answer:

Question a

A vehicle rated 27 kWh/100 mi is <blank>more</blank> efficient than an electric car rated 38 kWh/100 mi.

Question b

The energy required to drive this electric car 240 miles is <blank>\(91.2\)</blank> kWh.

Question c

The cost to drive this electric car 450 miles is <blank>\(\$22.23\)</blank>.