Ah, another math problem involving trains! Let's give it a shot.

We have two trains, one moving at 60 mph and the other moving at 80 mph. The first train leaves the station at noon, while the second train departs an hour later on a parallel track.

To figure out when the second train catches up to the first train, we need to find the time it takes for that to happen.

Let's say "t" represents that time in hours (after noon). Since distance equals speed multiplied by time (d = s * t), we can set up two equations based on this information:

Equation 1: d1 = 60 * t (distance traveled by first train)

Equation 2: d2 = 80 * (t -1) (distance traveled by second train)

In Equation 2, we subtracted one hour from "t" because it left an hour later than the first train.

Now, since they are meeting each other at some point where their distances are equal:

d1 = d2

Substituting our expressions for d1 and d2 into this equation:

60 * t = 80 * (t -1)

Simplifying and solving for "t":

60t = 80(t -1)

60t =