Jogging a hill
I think I originally heard this one on Car Talk.
Sally has decided to go for a jog. At first she runs on completely flat ground, and then to the top of a hill. Then she turns around and runs back exactly the same way she came: down the hill and back to her apartment. When she gets home she realizes she has ran for exactly 1 hour.
Sally knows she can run at 8 miles an hour on flat terrain, at 6 miles an hour going up hill, and 12 miles an hour running down hill. How many miles did Sally run?