Need to calculate % of involvment

I need to ask for a quick formula from everyone.

I have 4 dates:

A1 = Date of Project Start

B1 = Date of Project End

C1 = Date Student joined Project

D1 = Date Student left Project.

I have to figure out what percentage of the project the student participated in.

For MOST students A1 = C1 and B1 = D1, but I need to figure out the percentages for students where this is not true. I have a formula for students who joined late but stayed to the end, but it gives junk results for ones who either joined at start and left early or ones who both joined late and left early.