Halloween problem: A boy is lost in a haunted house. He is in a room with three doors. If he takes door A, he will find his way out of the house in 20 minutes. If he takes door B, he will find his way out of the house in 40 minutes. If he takes door C, he will wander around the house for 30 minutes and then wind up in the same room as he started in. Whenever he is in that room he picks doors A, B, and C with respective probabilities 0.1, 0.3, and 0.6. How long will it take, on average, to get out of the house?