Answer
$28.8$ miles per gallon
Work Step by Step
The average full efficiency for all the driving is:
$$\text{Average efficiency}=\dfrac{\text{total distance}}{\text{total amount of gasoline}}.$$
The total distance is $d$.
The amount of gasoline used on the distance traveled in highway driving is $(d/2)/36=d/72$, and the distance traveled in city driving is $(d/2)/24=d/48$.
Calculate the average efficiency:
$$\dfrac{d}{\dfrac{d}{72}+\dfrac{d}{48}}=\dfrac{d}{\dfrac{48d+72d}{72\cdot 48}}=\dfrac{d}{\dfrac{120d}{3456}}=\dfrac{3456}{120}=28.8.$$
So the average fuel efficiency is $28.8$ miles per gallon.
