It is Saturday morning, and you want to cook for next week. You share a kitchen with your roommate, but only one of you can cook there at the same time. Your roommate woke up before you did, and she started cooking at 11:00 am. The amount of time it takes your roommate to finish cooking is exponentially distributed with mean of 40 minutes. You decide to call your parents and talk to them until 11:50 am. If your roommate is still cooking, when you finish talking to your parents, you must wait for her to finish cooking before you start cooking.

If the amount of time you spend cooking is exponentially distributed with mean of 55 minutes, at what time do you expect to finish cooking?