Question

two trains leave stations 210 miles apart at the same time and travel tword each other. one train at 85 miles per hour while the other travels at 65 miles per hour. how long will it take for the two trains to meet?

Answer 1

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.

$\bf \begin{array}{lcccl} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ \cline{2-4}&\\ \textit{Train A}&d&85&t\\ \textit{Train B}&210-d&65&t \end{array}\\\\ \dotfill\\\\ \begin{cases} \boxed{d}=85t\\ 210-d=65t\\[-0.5em] \hrulefill\\ 210-\boxed{85t}=65t \end{cases} \\\\\\ 210=150t\implies \cfrac{210}{150}=t\implies \cfrac{7}{5}=t\implies \stackrel{\textit{one hour and 24 minutes}}{1\frac{2}{5}=t}$