Tricky Averages

Suppose the family uses each car to travel 120 miles. The first car would consume $120/30 = 4$ gallons and the second $120/40 = 3$ gallons, in which case a total of 240 miles has been travelled using 7 gallons, giving an average of $240/7 = \boxed{34.3}$ mpg to 1 decimal place.

Let the same distance traveled by the two cars be $d$ and the gallons of fuel consumed by the two cars be $v_1$ and $v_2$ such that $\dfrac d{v_1} = 30$ mpg and $\dfrac d{v_2} = 40$ mpg. Then the average mileage for the two cars is $\dfrac {2d}{v_1+v_2} = \dfrac {2d}{\frac d{30}+\frac d{40}} = \dfrac {240}7 \approx \boxed{34.3}$ mpg.

The best way to do this problem is with the harmonic average formula, which says to divide the number of terms n by the sum of the reciprocal of each of the terms. In our case, it'd be: $\frac{2}{(1/30) + (1/40)}$ , which approximates to 34.3.