Question

At noon a train leaves Bridgton heading east at 90 mi/h to Cogsville, 450 mi away. At 12:15 PM a train leaves Cogsville heading west to Bridgton at 100 mi/h. At what time will they pass each other?

Answer 1

Try drawing a picture. That always helps me.

Answer 2

This is a distance = weight * time situation that you'll want to reduce down to a single equation with only time as the unknown. Here's a start:
The noon train will travel distance, D=90T in T hours. Since you're looking for when they pass, the two together take up the whole 450mi. so the Cogsville train travels (450-D) miles in that time.
The d=r*t equation for the Cogsville train is therefore 450-D = 100(T-0.25). The T-0.25 is because it starts a quarter of an hour later.
Use those two equations to solve for T and translate that into clock time to answer the question.