Suppose two people A,B are assigned to do an individual task and then a group task.
Person A completes his individual task on average around 30 minutes. Person B completes his individual task on average around 40 minutes. After a person completes his individual task, he will move on to the group task. The group task can be completed alone by either A or B on average around 1 hour. The group task can be completed together on average around 30 minutes.
What is the expected time to finish all tasks?
My attempt: I know that it should be a max time it takes for the individual tasks to be done + additional time to finish group task.
I would have
E(max(A,B)) + E(T) where A is time it takes A for his own task and B is time it takes for his own task. The trouble I am having is conditioning on T, which is additional time to do the group task after all individual tasks have been finished.
I know that if can be broken up into two cases and further into two mini-cases:
Case 1: A>B Our time will be A if A > B + T. Our time will be A + T if A < B + T.
Case 2: B>A Our time will be B if A > B + T. Our time will be B + T if A < B + T.
I am not sure how to represent E(T) from here. Intuitively, seems like E(T) could be (0 + Average Time it Takes to Complete Group Task Together) divided by 2, so E(T) = 15 minutes.
Hence my answer would be E(max(A,B)) + E(T) = E(A+B-min(A,B)) + E(T) = 30 + 40 - 120/7 + 15 = 475/7 minutes.
Is my reasoning correct?