For those who were distracted or otherwise missed that lecture, the point is that it takes a defined amount of energy to move a body of mass over a measured distance. The speed of the object is not taken into account. Therefore, running and walking should require the same amount of energy to cover the same distance.
This is usually presented as great news for walkers. “Take a stroll around the block,” the thinking goes. “It’ll burn just as many calories mile for mile as if you sprinted it.” The only problem with this doctrine is that it is absolutely not true.