You and your friend are at a ski resort with two ski runs, a beginners run and an experts run. Both runs begin at the top of the ski lift and end at the finish line at the bottom of the same lift. Let h be the vertical descent for both runs. The beginners run is longer and less steep than the experts run. You and your friend, who is a much better skier than you, are testing some experimental frictionless skies. To make things interesting, you offer a wager that if she takes the experts run and you take the beginners run her speed at the finish line will not be greater than your speed at the finish line. The conditions are that you both start from rest at the top of the lift and both of you coast for the entire trip. Who wins the bet?