Question

Your car gets 25 mi/gal around town and 30 mi/h on the highway. If 60% of the miles you drive are on the highway and 40% are around town, what is your overall average miles per gallon?

Answer 1

60% = 0.6, 40% = 0.4. Your total mileage is D. We don't need to know the value of D, for reasons which will become apparent later. 0.6D is the mileage you drive on the highway, and 0.4D is the mileage you drive around town. You'll use 0.6D/30 gallons driving on the highway, and 0.4D/25 gallons driving on the street. Overall average miles per gallon is just the total distance driven divided by the number of gallons used:

\[\text{mpg} = \huge\frac{D}{\frac{0.6D}{30}+\frac{0.4D}{25}}\]The D in the numerator cancels out the Ds in the denominator, leaving \[\text{mpg} = \huge\frac{1}{\frac{0.6}{30}+\frac{0.4}{25}}\]When we make a common denominator for the two fractions, it becomes\[\text{mpg} = \huge\frac{1}{\frac{0.6}{30}*\frac{25}{25}+\frac{0.4}{25}*\frac{30}{30}}\]and when we divide by a fraction, we just invert the denominator and multiply instead, so
\[\text{mpg} = \frac{30*25}{0.6*25+0.4*30} =\]

If you want to verify the answer, go through the problem with total mileage = 3000 miles, find the distance driven on highway and street, and the gallons of gas used. Divide 3000 by the total gallons used, and you should get the same answer, if you didn't make a mistake anywhere.

Answer 2

@whpalmer4 Thank you so much! This was very logical and helpful! By doing this, I get 27.7 miles per gallon for the initial equation, correct?

Answer 3

Yes, though I would round to 27.8 since the answer was 27.7777777...