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 as 34 kwh/100 mi.
a. is a vehicle rated 21 kwh/100 mi more or less efficient than the electric car?
b. how much energy (in kilowatt-hours) is required to drive this electric car 250 miles?
c. assuming electricity costs \\$0.17/kwh, how much does it cost to drive this electric car 250 miles?

a. a vehicle rated 21 kwh/100 mi is more/less efficient than an electric car rated 34 kwh/100 mi.
b. driving 250 miles requires kwh.
c. it costs \\$ to drive 250 miles.
(round to the nearest cent as needed.)

Explanation:

Compare energy efficiency ratings

Using the Energy Efficiency Rating knowledge point
An energy efficiency rating of \(\text{kWh}/100\text{ mi}\) measures the amount of energy consumed per unit of distance. A lower value means less energy is consumed to travel the same distance, which represents higher efficiency.
Comparing a vehicle rated at \(21\text{ kWh}/100\text{ mi}\) to an electric car rated at \(34\text{ kWh}/100\text{ mi}\):

$$ 21\text{ kWh}/100\text{ mi} < 34\text{ kWh}/100\text{ mi} $$

Since \(21\) is less than \(34\), the vehicle rated at \(21\text{ kWh}/100\text{ mi}\) consumes less energy and is therefore more efficient.

Calculate energy required for 290 miles

Using the Dimensional Analysis and Unit Conversion knowledge points
We calculate the energy required for the electric car rated at \(34\text{ kWh}/100\text{ mi}\) to drive \(290\text{ miles}\):

$$ \text{Energy} = 290\text{ mi} \times \frac{34\text{ kWh}}{100\text{ mi}} $$

$$ \text{Energy} = 2.9 \times 34\text{ kWh} = 98.6\text{ kWh} $$

Calculate driving cost for 250 miles

Using the Dimensional Analysis and Unit Conversion knowledge points
First, find the energy consumed by the electric car rated at \(34\text{ kWh}/100\text{ mi}\) over \(250\text{ miles}\):

$$ \text{Energy} = 250\text{ mi} \times \frac{34\text{ kWh}}{100\text{ mi}} = 2.5 \times 34\text{ kWh} = 85\text{ kWh} $$

Next, calculate the total cost using the electricity rate of \(\$0.178/\text{kWh}\):

$$ \text{Cost} = 85\text{ kWh} \times \$0.178/\text{kWh} = \$15.13 $$

Answer:

Question 1

A vehicle rated \(21\text{ kWh}/100\text{ mi}\) is <blank>more</blank> efficient than an electric car rated \(34\text{ kWh}/100\text{ mi}\).

Question 2

Driving \(290\text{ miles}\) requires <blank>98.6</blank> \(\text{kWh}\).

Question 3

It costs \$<blank>15.13</blank> to drive \(250\text{ miles}\).