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They follow the cart tracks to the road and then brush the sand off themselves so they don't leave a trail.
The Boy finds some sand on the road, showing them which way the thief (or thieves) went.
They jog for a bit but The Man's lungs are too far gone. They walk.
The Boy wants to know if they're going to kill whoever has the cart.
They find the thief "deep into the long dusk" (355.1). He stands in front of the cart with a butcher knife. The Man has the pistol out. He tells the thief to back away from the cart and take his clothes off.
The Boy is crying; he doesn't want The Man to kill the thief. The Man makes the thief put his shoes and clothes in the cart. They leave him naked in the middle of the road.
Further down the road, The Boy is still crying. The Man tries to get him to stop, but can't. He tries to reason with The Boy, but The Boy thinks they've left the thief to die. Here's a pretty important exchange between our two main characters:
[The Man:] You're not the one who has to worry about everything. [...] He looked up, his wet and grimy face. Yes I am, he [The Boy] said. I am the one.
They walk back up the road and call to the thief, but no one answers. They keep calling. The Man finally just puts the thief's clothes and shoes in the middle of road.
They make camp for the night. The Man heats their supper on the burner. He tells The Boy that he wasn't going to kill the thief. The Boy answers: "But we did kill him" (358.1).
They set out again. The following night The Man wakes up. The Boy is also awake but doesn't really want to talk to The Man.
The Man walks out into the road and realizes how unmoored they are from time or anything else that steadied people in the former world. He also realizes that his own death isn't far off.
They keep going. In three days they come to a port town. The Man tries to find something with vitamin D for The Boy so he doesn't get rickets (softening of the bones – vitamin D helps your body absorb calcium, which strengthens the bones). No luck. The Boy still seems down.