2.78 Person A and Person B start at the same time and place, walking in opposite directions, and each reaches their respective destination A and B after one hour. If they still start from the original place and swap their destinations, then Person A arrives at destination B 35 minutes after Person B reaches destination A. The ratio of Person A's speed to Person B's speed is
(A) $7: 12$.
(B) $12: 17$.
(C) $3: 4$.
(D) $4: 3$.
(China Hubei Province Huanggang Junior High School Mathematics Competition, 1991)
[Solution] Let the speeds of person A and person B be $v_{1}, v_{2}$, respectively. According to the problem, we have
$$
\frac{60 v_{2}}{v_{1}}=\frac{60 v_{1}}{v_{2}}+35,
$$

If we set $\frac{v_{1}}{v_{2}}=t$, then the above equation can be transformed into
$$
\frac{60}{t}-60 t-35=0 \text {, i.e., } 12 t^{2}+7 t-12=0 \text {. }
$$

Solving this, we get $t_{1}=\frac{3}{4}, \quad t_{2}=-\frac{4}{3}$ (discard $t_{2}$).

Therefore, the answer is $(C)$.