When will velocities of the trains equal?

[Entr0py]

Homework Statement

A train having a velocity of x m/s is caught by a train accelerating from zero 20 seconds after the second train starts. At what time were their velocities equal?

Homework Equations

The Attempt at a Solution

I was thinking that you'd have to assume that the train with x velocity is traveling with constant velocity and that the second train starts at t=t-20 s. However, I'm confused as to how I would find when their velocities would be equal.

 

[Bystander]

How far does the first train travel?

 

[Entr0py]

So in 20 s, the first train has traveled x=x0+v0t+.5at^2. well I assumed it started from rest, so x=.5a(400) or 200a m.

 

[Bystander]

I'd call that the second train from my reading of the problem statement. Let's tidy up the statement a bit so we're both discussing the same trains. "Train A is moving at a constant velocity of x m/s. As it pulls even with Train B, Train B accelerates from 0 at a constant rate, and pulls even with A after 20 seconds. At what time are the two velocities equal?"

Now, I ask how far does Train A travel?

 

[Entr0py]

I'm sorry I'm confused?

 

[haruspex]

I'm sorry I'm confused?

You need to say exactly what is confusing you. Bystander's description of the problem is correct. I'll try to make it more concrete.
At t=0, both trains are at s=0. Train A is moving at constant speed x, train B is stationary.
Train B then accelerates at some unknown constant (we must assume) rate a. At t=20, the trains have traveled the same distance. Train B must now be moving faster than train A.
At what time was train B moving at speed x?

Bystander is asking you, first, how far train A traveled in those 20 seconds.