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.

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.