In the end, Kate was too scared to be rejected as a woman, so she didn't do anything and just helped Billy with his research earnestly. The only problem was that the information regarding states very far away from them was rather old. Billy felt like a fool waiting for more than that.
Before long, Billy noticed that it was the middle of the afternoon, and they had skipped their lunch. Aura probably assumed that they weren't hungry and didn't send anyone to bother them.
"I suppose any information is better than nothing… even if it is old," Billy said. "Let's finish things here, Kate… Kate?"
Billy felt a gentle touch on his left shoulder, and then he realized that Kate had fallen asleep right here. It was a bit too soon for Kate to feel sleepy, so Billy imagined that she was trying to appeal to him, but then she began to snore.
"How can you snore while sleeping like this?" Billy asked and then laughed.