You are working on a programming project with your partner for a computer science course. The project is due in $48$ hours. Together, you are to produce a computer program and each of you are assigned to write a portion of computer code. Both of you work simultaneously, but independently. The completion time of your task follows a uniform distribution between $30$ and $50$ hours. Your partner is stronger in programming and his task is more complex, and the completion time for his task follows a uniform distribution between $34$ and $55$ hours.