algebra precalculus - Comparing the time in the time-distance problem

The question is:

Two trains start at point A and B and travel towards each other at a speed of $50$km/hr and $60$Km/hr respectively. At the time of meeting the second train has traveled $120$ km more than the first train. Now the distance between them is:

Now I did manage to solve it with a little help and its like this:

First Train starting from $A$:

$t = x/50$

Second Train starting from $B$:

$t = (120+x) / 60$

Comparing $A$ and $B$ we get $x$ and then using the value of $x$ we can calculate the total distance between them which is $1320$.

My question is why are we comparing $A$ and $B$. The only reason we would compare them is if they were equal. I don't understand how time could be equal when the two trains meet. I would appreciate it if someone could kindly clarify this concept.

Answer

It is important that both the trains start at the same time instant. Hence, when they meet, both trains would have taken the same time.