Respuesta :
recall your d = rt, distance = rate * time.
let's say we have two trains, A and B, A is going at 85 mph and B at 65 mph.
they are 210 miles apart and moving toward each other, at some point they will meet, when that happens, the faster train A has covered say d miles, and the slower B has covered then the slack from 210 and d, namely 210 - d.
When both trains meet, A has covered more miles than B because A is faster, however the time both have been moving, is the same, say t hours.
[tex] \bf \begin{array}{lcccl}
&\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\
\cline{2-4}&\\
\textit{Train A}&d&85&t\\
\textit{Train B}&210-d&65&t
\end{array}\\\\
\dotfill\\\\
\begin{cases}
\boxed{d}=85t\\
210-d=65t\\[-0.5em]
\hrulefill\\
210-\boxed{85t}=65t
\end{cases}
\\\\\\
210=150t\implies \cfrac{210}{150}=t\implies \cfrac{7}{5}=t\implies \stackrel{\textit{one hour and 24 minutes}}{1\frac{2}{5}=t} [/tex]
