recall your d = rt, distance = rate * time
so, keeping in mind that both trains are going at the same speed, say speed of "r" mph, after 212 hours A arrived at station A and after 4 hours, B arrived at station B.
now, the distance covered by train A is say "d", we know both stations are 585 miles apart, so, if train A covered "d" miles in those 212 hours, then train B covered the slack from 585 and d, that is "585 - d".
[tex]\bf \begin{array}{lccclll}
&\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\
&------&------&------\\
\textit{Train A}&d&r&212\\
\textit{Train B}&585 - d&r&4
\end{array}
\\\\\\
\begin{cases}
\boxed{d}=212r\\
585-d=4r\\
----------\\
585-\boxed{212r}=4r
\end{cases}
\\\\\\
585=216r\implies \cfrac{585}{216}=r\implies \cfrac{65}{24}=r\implies \stackrel{mph}{2\frac{17}{24}}=r[/tex]
