Let t be the time in hours for which the two trains meet, then we can set the following equation:
[tex]85t+65t=180.[/tex]Solving for t we get:
[tex]\begin{gathered} 150t=180, \\ t=\frac{18}{15}=\frac{6}{5}\text{.} \\ t=1.2. \end{gathered}[/tex]Answer: 1.2 hours.