11.9 Cost to Drive

Example one: 
How much does it cost to drive a gas car?

Assume your vehicle gets 25MPG and gasoline costs $3.75/gallon. How much does it cost you to drive per mile?

Hint: Remember back to Lesson 2: When we learned about conversions. We can consider our 25 miles/gallon and $3.75/gallon just more conversions.

We want our answer to have units of $/mile, so we need to find a way to get the gallons to cancel out.

$$\begin{gathered} \left(\frac{\$3.75}{\bcancel{\mathrm{gallon}}}\right)\times \left(\frac{\bcancel{\mathrm{gallon}}}{25\text{ miles}}\right) \\ =\left(\frac{\$3.75}{25\text{ miles}}\right) \\ =\frac{\$0.15}{\text{mile}} \end{gathered}$$

It costs about 15 cents per mile driven in this situation.

Example two:
How much does it cost to drive an electric car?

An electric vehicle requires 30 kWh to drive 100 miles. If you charge in your home, where electricity cost $0.18/kWh, how much does it cost to drive per mile? 

Once again, we can look at the givens just like conversion factors. In this case the fuel efficiency of an EV is given as 30kWh/100 miles.   

Remember we are looking at solving for $/mile again, so follow the units.

$$\begin{gathered} \frac{\$0.18}{\bcancel{\text{kWh}}}\times \frac{30\bcancel{\text{kWh}}}{100\text{ miles}} \\ \frac{\$0.18\times 30}{100\text{ miles}} \\ \frac{\$5.40}{100\text{ miles}} \\ \frac{\$0.054}{\text{mile}} \end{gathered}$$

= ~ $0.054/ mile or about 5.4 cents per mile to drive electric

Example 3:  
Real life comparison EV versus Gasoline

You live in an off-campus apartment 5 miles from campus. You drive the 10-mile round trip 4 days a week, plus another 200 miles a week for weekend errands, hanging out with friends, and part-time job commuting. Assume gasoline is $4.25/gallon in your area and electricity costs $0.16/kWh. Compare the cost to drive per month via gasoline powered vehicle that gets 30 MPG and electricity in a car that gets 32 kWh/100 miles.

Estimated monthly driving: 40 mile/week to class = 160 miles/month +800 miles/month

Estimated ~ 1000 miles/month ** (rounded up from 960)

Cost to drive a gas car for a month ($/month)

$$\begin{gathered} \left(\frac{1000\bcancel{\text{miles}}}{\text{month}}\right)\times \left(\frac{1\cancel{\text{gallon}}}{30\bcancel{\text{miles}}}\right)\times \left(\frac{\$4.25}{1\cancel{\text{gallon}}}\right) \\ =\left(\frac{1000}{\text{month}}\right)\times \left(\frac{1}{30}\right)\times \left(\frac{\$4.25}{1}\right) \\ =\left(\frac{1000\times 1\times \$4.25}{30\times 1}\right)/\text{month} \\ =\left(\frac{\$4250}{30}\right)/\text{month} \\ =\$141.67/\text{month} \end{gathered}$$

It will cost $141.67/month to drive a gas car.

Cost to drive an electric car for a month ($/month)

$$\begin{gathered} \left(\frac{1000\bcancel{\text{miles}}}{\text{month}}\right)\times \left(\frac{32\cancel{\text{kWh}}}{100\bcancel{\text{miles}}}\right)\times \left(\frac{\$0.16}{1\cancel{\text{kWh}}}\right) \\ =\left(\frac{1000}{\text{month}}\right)\times \left(\frac{32}{100}\right)\times \left(\frac{\$0.16}{1}\right) \\ =\left(\frac{1000\times 32\times \$0.16}{100\times 1}\right)/\text{month} \\ =\left(\frac{\$5120}{100}\right)/\text{month} \\ =\$51.20/\text{month} \end{gathered}$$

It will cost $51.20/month to drive an electric car.

The monthly savings of driving an electric car versus gasoline in this scenario is $141.67-$51.20, or $90.47/ month.  Remember this depends on how much you drive and the cost of fuel.  If you charge at a fast-charging station, prices would be significantly higher to drive electric.