Algebra 2
posted by Mia on .
Your car gets 25 mi/gal around town and 30 mi/gal on the highway.
a. If 50% of the miles you drive are on the highway and 50% are around town, what is your overall average miles per gallon?
b. If 60% of the miles you drive are on the highway and 40% are around town, what is your overall average miles per gallon?

a. Since the miles are equal, then you can just average your gas mileage.
b. This will be a weighted average.
Say you travel 100 miles.
60(30) + 40 (25) =
Divide that answer by 100. 
if you drive c city miles and h highway miles, the gas you use is
c/25 + h/30 gallons
so, for a 5050 mix
100mi/(50/25+50/30)gal = 27.27 mi/gal
and for a 4060 mix
100mi/(40/25+60/30)gal = 27.77 mi/gal
extra credit:
So, what would the mix have to be to get 29 mi/gal? 
JJ's solution sounds simple, but the reality is not. This is just like the usual work problems. If A can do a job in 2 days, and B can do it in 4 days, you can't just average 2 and 4 to get 3 days.
Instead, 1/both = 1/A + 1/B = 1/2 + 1/4 = 3/4
So, together they do the job in 4/3 days.
Makes sense, since A alone can do it in 2 days, any help from B will reduce the time it takes, not average out to 3 days.
Same for the gas mileage.
50 miles at 25gal/mi = 2 gal
50 miles at 30mi/gal = 1.6667 gal
so, 100 miles takes 3.6667 gal, or 27.27 mi/gal 
Thank you so much, Steve!!!! I really appreciate your help!!