$1 \cdot 110$ The distance from $A$ to $B$ is 120 miles, a car travels from $A$ to $B$ at a speed of 30 miles per hour; and from $B$ back to $A$ at a speed of 40 miles per hour, then, the average speed for the round trip is
(A) $33 \mathrm{mph}$.
(B) $34 \mathrm{mph}$.
(C) $35 \mathrm{mph}$.
(D) $36 \mathrm{mph}$.
(E) $37 \mathrm{mph}$.
( mph stands for miles per hour)
(1st American High School Mathematics Examination, 1950)
[Solution] If a car travels a distance $d$ at a speed of $v_{1}$, and returns the same distance at a speed of $v_{2}$, then the average speed for the round trip is
$$
\bar{v}=\frac{2 d}{\frac{d}{v_{1}}+\frac{d}{v_{2}}}=\frac{2 v_{1} v_{2}}{v_{1}+v_{2}}.
$$

Therefore, $\bar{v}=\frac{2 \cdot 30 \cdot 40}{30+40}=\frac{2400}{70} \approx 34(\mathrm{mph})$.
So the answer is $(B)$.