Mac and cheese. While Juanita waits for her Mac and Cheese to boil, she works on her homework for 1/2 of the time. She has been waiting for 3 minutes already (so she has already done 1.5 minutes of homework). She doesn't know how much more time is needed. She estimates that the remaining time (in minutes) until the water boils is an Exponential random variable Y with density otherwise.
Find the total length of time that she expects to work on her homework while waiting for the water to boil.