Question

Two trains leave the station at the same time one heading west and the other east. The westbound train travels 12 miles per hour faster than The eastbound train. If the two train are 760 miles apart after 4 hours, what is the rate of the westbound train?
Do not do any rounding

Answer 1

Recall your d = rt, distance = rate * time.

let's say the Eastbound train is going at a rate of "r" mph, since we know the Westbound train is going faster 12 miles more than that, then the Westbound train must be going "r+12".

we also know that after 4 hours, both of them were 760 miles apart, so

$\bf \begin{array}{lccclll} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ &------&------&------\\ Westbound&760&r+12&4\\ Eastbound&760&r&4 \end{array} \\\\\\ \begin{cases} 760=(r+12)(4)\implies 190=r+12\\ 760=4r\implies 190=r \end{cases} \\\\\\ \textit{since we know that r = 190, then }\qquad \stackrel{Westbound}{190+12}$