3.29 Two lines intersect perpendicularly at point $O$, and $A, B$ move along these two lines at uniform speeds. When $A$ is at point $O$, $B$ is 500 yards away from $O$. After 2 minutes, they are equidistant from $O$. After another 8 minutes, they are still equidistant from $O$. The ratio of $A$'s speed to $B$'s speed is
(A) $4: 5$.
(B) $5: 6$.
(C) $2: 3$.
(D) $5: 8$.
(E) $1: 2$.
(19th American High School Mathematics Examination, 1968)
[Solution] Let $u, v$ represent the speeds of $A, B$ respectively. According to the problem, after 2 minutes and 10 minutes, they are equidistant from $O$, as shown in the figure $O A^{\prime}=O B^{\prime}, O A^{\prime \prime}=O B^{\prime \prime}$. That is,
$$
\left\{\begin{array}{l}
2 u=500-2 v, \\
10 u=10 v-500 .
\end{array}\right.
$$
(1) + (2) gives $12 u=8 v$,

which means $u: v=2: 3$.
Therefore, the answer is $(C)$.