Markov Chains & Long-Run Behavior · Challenge problem

Weather in a town follows a Markov chain: after a dry day the next day is rainy with probability $1/4$, and after a rainy day the next day is rainy with probability $1/2$. Today is dry. What is the expected number of days, counting from tomorrow, until the first time there have been two rainy days in a row (counting the second of those two days)?