Trains A and B are traveling in the same direction on parallel tracks. Train A is traveling at 40 miles per hour and train B is traveling at 60 miles per hour. Train A passes a station at 12:20 A.M. If train B passes the same station 12:32 A.M at what time will train B catch up to train A?
What time will train B catch up with train A?

Are you sure this is a word problem?
Sounds more like a math problem to me.

either way I am called and heading out to run train A for a couple hundred miles, I will let you know when I pass the station. :=)

You are correct about this being a "word" problem in the subject of Mathematics. However, just because it contains the word "train" in the problem does not mean it should be posted in the "Rail" subsection of the "Transportation" category. It is a "Homework Help" question, and that is where you should ask it..

As it's been pointed out, you asked this in the wrong place, but here's the answer and, more importantly, how to GET the answer--

Train A is 12 minutes ahead of Train B at 12:32 (12:32 - 12:20). Next, figure how far ahead Train A is. One way is to say that if it's moving at 40 mph, that equals 2/3 miles per minute (40 mi/h / 60 min/hr). After 12 minutes, Train A is 8 miles away (12 min * 2/3mi/min).

Train B is catching up to Train A at the rate of 20 mph (60 mph - 40 mph). 20 mph is 1/3 miles per minute (20 mi/h / 60 min/hr). 8 miles / 1/3 miles per minute = 24 minutes. From 12:32, 24 minutes would be 12:56am (12:32 + 24 min).

If that doesn't make sense, try this. Train A has a 12 minute head start on Train B when Train B passes the station at 12:32 (12:32 - 12:20). 12 minutes is 1/5 of an hour (12/60). If Train A would take 1 hour to go 40 miles, it can go only 1/5 as far in 1/5 of an hour, or 8 miles (40 * 1/5).

Train B catches up to Train A at 20 miles per hour (60mph - 40mph). Train B could make up 20 miles of distance in an hour, but only has to make up 8 miles, so should only take 8/20 of an hour to make up the 8 mile gap. 8/20 is the same as 24/60, and 24/60ths of an hour is 24 minutes, so from 12:32, it'll take until 12:56am for Train B to catch Train A (12:32 + 24 min).

It's a good thing it's mentioned in the problem that the trains are on parallel tracks, or there's going to be a train wreck at 12:56am!