Ana can paint a house in three hours. Ana paints a house for an hour and then Joe joins her. The house gets painted in a total of two hours. How long would it take Joe to paint a house by himself?

Answer 1

joe alone will paint the house in 3 hours, just like Ana

After one hour alone Ana paints 1/3 of the house, leaving 2/3 left

Together they paint 2/3 of the house in 1 hour. Since Ana pains 1/3 in 1 hour, that left the other 1/3 (2/3-1/3) to be painted by Joe in 1 hour. They both paint at the same rate, one house per 3 hours

(unless you interpreted the problem to mean they both painted the remaining 2/3 of a house in 2 hours. Ana alone in 1 hour for 1/3 of the house, then both painting together to finish it in a 2 more hours. Then Joe fell asleep and Ana did the whole house. 1/2 + 1/J = 1/2, with J= an infinite time to paint the house. But that interpretation is most unlikely)