Question 58·200 Super-Hard SAT Math Questions·Problem Solving and Data Analysis

A unit rate tells you the amount for one kilometer. Type $h=\frac{5.6}{100}$. Desmos shows $h=0.056$ liter per kilometer, so $h$ is the highway fuel-use rate.

25% more gasoline per kilometer means the city rate is $125\%$ of the highway rate: the original $100\%$ plus $25\%$. Type $c=125\%\operatorname{of}h$. Desmos shows $c=0.07$ liter per city kilometer. Don't increase miles per gallon by $25\%$; that rate runs in the opposite direction.

The city rate uses kilometers, so change the $50$ city miles to kilometers. Type $d=50(1.609)$. Desmos shows $d=80.45$ kilometers, the distance to use with $c$.

Multiply each distance by its own fuel-use rate, then add: $80h$ is highway liters and $dc$ is city liters. Type $g=80h+dc$. Desmos shows $g=10.1115$ liters for the whole trip.

Miles belong on top of miles per gallon. Since each mile is $1.609$ kilometers, divide the $80$ highway kilometers by $1.609$, then add the $50$ city miles. Type $m=\frac{80}{1.609}+50$. Desmos shows $m\approx99.72$ miles.

The bottom must be gallons, so divide $g$ liters by $3.785$ liters per gallon. Type $\frac{m}{g/3.785}$. Desmos shows about $37.33$ miles per gallon, which rounds to $37$ miles per gallon for the entire trip. Choice D.