The relationship between the speeds of two individuals, $P_1$ and $P_2$, can be expressed as $\frac{S_1^2 + S_2^2}{S_1^2 - S_2^2} = \frac{3^2 + 4^2}{3^2 - 4^2}$, where 3 and 4 are constants. Determine the ratio of the times $t_1$ and $t_2$, which represent the durations taken by $P_1$ and $P_2$ to traverse the same distance at speeds $S_1$ and $S_2$ respectively.