If you can't get more energy out of a system than you put in, why can humans travel faster and farther on

a bike than on foot? Isn't the same amount of energy being expended?

Your question makes a lot of assumptions, but let's say you've got a perfectly flat surface to work with. A person walking a mile expends energy not just propelling himself forward, but also supporting his own weight and maintaining his balance. The person on the bike has at least part of his weight supported by the bicycle seat and even the pedals, which partially support his legs. Also, the energy is expended in a different way -- rather than pushing back against the ground to move forward, it is utilizing a mechanical advantage from the bicycle to convert the up and down motion of his legs into rotational motion on the wheels. The bike, moreover, must overcome rolling friction, which is generally less than the static friction he must overcome on foot. So the bicycle rider exerts less energy than the walker to travel the same distance because the bicycle gives him a mechanical advantage. Per un