If a person ran 3-4 miles in 30 minutes, would the same person burn the same amount of calories as walking 3-4 miles in about an hour?

Would walking up a very steep hill for 1 mile actually make a person burn more calories per mile than someone running on a very flat terrain?

Can't say. It depends on the person and on what their heart rate is while they're doing the exercise. Everyone burns calories differently.

depends on way too many factors to answer. what burns more for some will burn less in others.

If you're asking this in terms of what should I do, then do whatever you find to be more intense. Thats what works best, pushing your intensity levels to make sure the bodies energy systems are fully utilized and taxed.

Pretty much the only difference is the time taken to do the distance. Calorie burn is pretty much the same i think.
I prefer to get it over and done with, the quicker the better!

However on that note: speeding things up does make you feel better, and gives your metabolism a kickstart for the rest of teh day

Thanks! I thought that it was the same amount per mile walking vs/running, but I wanted to make sure. I found a cool calculator that compares the calorie burn of walking/running at different inclines etc ...at Free Calorie Counter, Weight Loss Calculators, and Weight Loss Tutorial | CaloriesPerHour.com

Good article referencing the subject of walking vs. running in relation to caloric cost.

How Many Calories Are You Really Burning? | From Runner's World

very nice article.