are open to her. The first passage leads to the outside after 1 hour of travel.

The second passage winds around and will return her to the same place

after 3 hours of travel. The third and final passage also winds around and

will return her to the same place after 5 hours of travel. If the hiker is at all

time equally likely to choose any one of the passages, what is the expected

length of time until he reaches the outside?

I know its 33% for each route. But I have no idea how to determine the final hour amount.

One could spend 10 hours in there going down the same route twice. or, you could spend 1 hour in there if you chose properly the first time.

The final answer is 7 hrs. I just have no idea how to get there