Ajet flew at an average speed of 480 mph from point x to point y. because of head winds, the jet averaged only 460 mph on the return trip, and the return trip took 30 minutes longer. how many hours was the flight from point y to point x? how far is it from point x to point y?

The distance is the same in both instances. 
Speed =distance/time
So distance=speed x time
Let's assume the jet took t hours from X to Y, it took t+0.5 hours from Y to X
Equate distance (speed x time) from X to Y to that from Y to X
480t=460(t+0.5)
480t=460t+230
20t=230
t=11.5hours
t+0.5=12hours(Hours taken to fly from Y to X)
Distance=speedxtime
            =460x12
            =5520m