Alright, lets get started.
The trip takes 13 hours for a car moving at 68 mph.
We could find the distance between both cities with help of this.
Distance = time * speed
Distance = 13 * 68 = 884 miles
Means the distance between both cities = 884 miles
Now if the trip takes 17 hours, we need to find new speed.
For finding this new speed, one thing that not changed is, distance between two cities that is 884 miles.
Speed = distance / time
Speed = 884 / 17
Speed = 52 miles / hr
Hence, the speed of the car is 52 miles / hr : Answer
Hope it will help :)