recall your d = rt, distance = rate * time
if say train B has a speed of "r", then A has a speed of "r-14".
now, they each travelled those miles in the same time, say "t" hours.
[tex]\bf \begin{array}{lccclll}
&\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\
&-----&---&----\\
\textit{Train A}&220&r-14&t\\
\textit{Train B}&290&r&t
\end{array}
\\\\\\
\begin{cases}
220=t(r-14)\\
290=rt\implies \frac{290}{r}=\boxed{t}\\
----------\\
220=\boxed{\frac{290}{r}}(r-14)
\end{cases}
\\\\\\
220=\cfrac{290(r-14)}{r}\implies 220r=290r-4060\implies 4060=70r
\\\\\\
\cfrac{4060}{70}=r\implies 58=r[/tex]
how fast is Train A? well, r - 14.
