Brad’s relationship with his girl friend Angelina changes between Amorous, Bickering, Confusion, and Depression according to the following transition rates when t is the time in months.

They are amorous now. What is the expected amount of time until depression sets in?
I am using the book by Durrett. There is a formula in the book for this type of question. However, I am not sure how to use it. We want to hitting time from state 0 to state 3.