A miner is trapped in a mine containing 3 doors. The first door leads to a tunnel that will take him to safety after 10 minutes of walking. The second door leads to a tunnel that will return him to the similar mine with 3 doors after 20 minutes of travel. The third door leads to a tunnel that will return him to the similar mine after 30 minutes. The miner has no idea which door is the safe exit and he cannot go back.

What is the expected time until he reaches safety?