a train travels due north at 65 km/h. Six hours later, 
another train leaves the same station travelling due 
north on a parallel track, and travels at 95 km/h.  
In how many hours will the second train overtake the 
first?

The way that question is asked, it could be taken two 
ways:

1. As the number of hours after the first train starts
OR
2. As the number of hours after the second train starts

I will assume it is 2. 

Make this chart

            DISTANCE    RATE    TIME
1st train |                          
2nd train |                         

Fill in the given rates (speeds):

            DISTANCE    RATE    TIME
1st train |              65        
2nd train |              95         

Let the time after the 2nd train starts be x hrs.
Fill that in for the 2nd train's time.

            DISTANCE    RATE    TIME
1st train |              65           
2nd train |              95      x

The 1st train travels for 6 hours longet than the
2nd train, so we add 6 hrs to x hrs and get x+6 hrs.
Fill that in for the 1st train's time:

            DISTANCE    RATE    TIME
1st train |              65     x+6
2nd train |              95      x

Now use D = RT to fill in the DISTANCES:


            DISTANCE    RATE    TIME
1st train |  65(x+6)     65     x+6
2nd train |  95x         95      x

The trains travel the same distance, so set the
two distances equal to each other:

65(x+6) = 95x

Solve that and get x = 13 hours after 2nd train leaves,
which is 19 hours after 1st train leaves.

Checking:

During the 6 hours the first train travels before the
second one starts, the first train will have moved 65×6
or 390 km down the track when the 2nd one starts.
In another 13 hours the first train will have moved 
an additional 65×13 or 845 km, making his total distance 
from the station 1235 km.  During that last 13 hours the
2nd train will move 95×13 or 1235 km.  So the two trains 
will be together at that time.   

Edwin