My Red Headed Step Child

I am only watching the one year old today. I think he is going to drive me nuts. When he doesn't have anyone to play with, he likes to wander the hallway crying. He won't play with any of the cars and he won't ride around on Clifford the Dog like he usually does when my son is around. If he is not whining in the hallway, he is standing next to me starring. If I play with him on the floor or give him some toys to play with, he ends up laying down and falling asleep. If I don't immediately wake him up, it's messes up his afternoon nap. What am I going to do with him? This happens every Thursday and I need to come up with something to appease the boy so I get through my daily household responsibilities without him under my feet. Any ideas?