Originally Posted by Jaywalk3r

Legs "get back the energy" on the downhills, which are "free" in terms of marginal costs. That is to say that once one summits the hill, they can typically coast back down with no additional effort, using only the potential energy stored from the climb.

The only real additional challenge hills provide is that the rider has to have enough energy to "pay for the downhills" in advance. For example, if we consider a ride that consists of one long climb and one long descent, with the summit at the midpoint. The rider has to be capable of expending enough effort in the first half of the ride. So, for the first half, climbing requires much more effort than riding the same distance in flat lands. For the second half, descending requires much less effort than riding the same distance in flatlands. But the rider must be capable of expending virtually all effort for the ride in the first half.

If we assume that riding on the flatlands is done at a constant speed, then the only difference in total energy expended is due to the difference in speed of climbing versus descending. Ironically, it is the descent where the extra energy is expended. If we allow the possibility that the rider in the flatlands is doing interval training instead of riding at a constant speed, we no longer have sufficient information to determine which ride required more energy.