Amey, these kinds of problems can be difficult to figure out.
The main thing to remember is our basic idea that distance = rate x time.
If we think about it, no matter how far each train travels, when they meet, they will have together travelled 390k.
If we let x = the time travelled by train A, then train B travels x - 1 hours, because it left one hour later.
Train A's distance is then 65x and train B's is 35(x - 1) = 35x - 35.
Together, the trains travel the 390k
65x + 35x - 35 = 390
100x - 35 = 390
100x = 425
x = 4.25 = 4 hours and 15 minutes
Soooo, the two trains meet at 2:15.
Hope this helps!