Expected Wait for Two Independent Train Lines

You arrive at a train station at a random time. Two train lines, $A$ and $B$, serve the station. Trains on line $A$ arrive according to a Poisson process with rate $\lambda_1$ (so the inter-arrival time is $\text{Exp}(\lambda_1)$), and trains on line $B$ arrive independently with rate $\lambda_2$ (inter-arrival time $\text{Exp}(\lambda_2)$). You board whichever train comes first, regardless of the line. 1. Find the expected time you wait until the next train arrives. 2. Evaluate your answer when $\lambda_1 = 1/10$ and $\lambda_2 = 3/20$.