An escape room participant, named Alice, is trapped in a room containing three doors. Assume that, at all times, Alice equally likely to choose any of the doors. The first door leads to a route that takes Alice to safety after 1 hour. The second door leads to a route that takes her back to the same room after 1 hour. The third door leads to a route that returns her back to the same room after 30 minutes. What is the expected length of time until she reaches safety?

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