SOLUTION: Two trains of equal length are on parallel tracks. One train is travelling at 40 km/h and the other at 20 km/h. It takes two minutes longer for the trains to completely pass on

Let's convert their speeds to km/minute

20 km/h =  km/minute =  km/minute
40 km/h =  km/minute =  km/minute


Let each train's length be x, and the time to pass when going in
opposite directions be t minutes.  Then the time to pass when going in
the same directions will be t+2.

Here they are going in opposite directions starting to pass each other:

  

Suppose the train on the left is the faster train.  For the train on the 
left to pass the train on the right, point A must move to be even with 
point B.  

Point A is approaching point B at a rate equal to the sum of the rates
or  or 1 km/minute. Point A's distance to point B is 2x.
Since distance = rate·time, we have 2x = 1·t

Here they are going in the same direction, the faster starting to pass
the slower.

  

Suppose again the train on the left is the faster train.  As above, for the
train on the left to pass the train on the right, point A must move to be 
even with point B.  In this case Point A is approaching point B at a rate equal
to the difference of the rates or  or  km/minute. Again, point A's distance 
to point B is 2x. Since distance = rate·time, in this case we have 2x = ·(t+2).

So we have this system of equations:

2x = 1·t
2x = ·(t+2)

Solve that system by substitution and get

x = 0.5 km, and t = 1 minute

Each train is 0.5 km long and it takes 1 minute for them to pass 
each other when going in opposite directions and 1+2 or 3 minutes 
for the faster to pass the slower when going in the same direction.

Edwin