Is Self Control a Depletable Resource in Humans?

In a study with kids, only a third of them were able to wait the ten minutes before the person come back. And it's in relation to self control, which is the core of trying to break a bad habit. They did another study with adults, and this one hasn't been as verified,. But they had two groups of people go into a room, and there was a plate of radishes, i think, and a plate of freshly baked chocolate chip cookies. The group that could eat whatever they wanted lasted half as long at solving the puzzle than the group that could ate whatever they wanted.