$2 \cdot 124$ A boat's speed in still water is $15 \mathrm{mph}$ (miles per hour), and the speed of a stream's current is $5 \mathrm{mph}$. If the boat makes a round trip over a certain distance, the ratio of the boat's average speed for the round trip to its speed in still water is
(A) $\frac{5}{4}$.
(B) $\frac{1}{1}$.
(C) $\frac{8}{9}$.
(D) $\frac{7}{8}$.
(E) $\frac{9}{8}$.
(5th American High School Mathematics Examination, 1954)
[Solution] Let the distance the boat travels be $d$, and the average speed be $x$. According to the problem, we have $\frac{d}{15+5}+\frac{d}{15-5}=\frac{2 d}{x}$, solving this yields $x=\frac{40}{3}$. Therefore, the ratio of average speed: still water speed $=\frac{40}{3}: 15=8: 9$. Hence, the correct choice is $(C)$.