I think that it would be 5 hours since:
If you calculate the average speed of both cars: (55mph + 65mph) = 120. 120/2 =60mph
And then they have 300 miles to travel and they are doing 60 miles in one hour (or 60mph).
So in 1 hour they will have travelled 60 miles.
In 2 hours they will have travelled 120 miles.
3 hours = 180 miles
4 hours = 240 miles
5 hours = 300miles
So the answer is 5 hours :-)