Question

Aj is traveling north on a road while Rogan is traveling south on the same road. they pass by each other at 3pm. Aj is traveling 30 mph and Rogan driving 40 mph. at what time will they be 105 miles apart?

Answer 1

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

both folks are traveling in opposite directions, Aj is northbound and Rogan is southbound.

we know Aj is going at a rate of 30mph and Rogan at 40mph, let's say that by the time they are 105 miles apart, Aj has covered "d" miles, then Rogan has covered the slack from 105 and "d", or "105 - d" miles.

let's also keep in mind they they both have been driving the same amount of time, say "t" hours.

$\bf \begin{array}{lcccl} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ &------&------&------\\ Aj&d&30&t\\ Rogan&105-d&40&t \end{array} \\\\\\ \begin{cases} \boxed{d}=30t\\ 105-d=40t\\ --------\\ 105-\boxed{30t}=40t \end{cases} \\\\\\ 105=70t\implies \cfrac{105}{70}=t\implies \cfrac{3}{2}=t\implies 1\frac{1}{2}=t$

when they passed each other, it was 3pm, by the time they are both 105 miles apart, they have been traveling for 1½ hours.  What time is it? well, is just 4:30pm.