\[5\ ч\ 20\ минут = 5\frac{1}{3}ч = \frac{16}{3}\ ч.\]
\[Составим\ систему\ уравнений:\]
\[\left\{ \begin{matrix} tx = 3 \cdot (x + 15) \\ t(x + 15) = \frac{16}{3}x \\ \end{matrix}\text{\ \ \ \ \ \ \ } \right.\ \text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }\]
\[\left\{ \begin{matrix} tx = 3x + 45\ \ \ \ \ \\ tx + 15t = \frac{16}{3}x \\ \end{matrix}\text{\ \ \ \ } \right.\ \]
\[\left\{ \begin{matrix} x = \frac{45}{t - 3}\text{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ } \\ \frac{3t}{t - 3} + t - \frac{16}{t - 3} = 0 \\ \end{matrix} \right.\ \]
\[\frac{3t - 16}{t - 3} + t = 0\]
\[3t - 16 + t² - 3t = 0\]
\[t^{2} = 16\]
\[t = \pm 4.\]
\[4\ часа - время\ встречи.\]
\[Ответ:4\ ч,\ \ \ 45\ \frac{км}{ч,\ \ \ 60\ \frac{км}{ч.}}\]