How to Proportion Rent When Tenant Moves Out?

I am renting out a room in my home and had a tenant move out without proper notice. According to Washington Landlord-Tenant law, she owes 30 days' rent from the time she moved out, or until I find a new renter, which may (hopefully) be soon. So to figure out how much each roommate owes, do I divide the monthly rent by 31? (Say we found old roomie moved out on the 3rd, and new roomie moves in on the 20th, then she owes 17 days and new roomie owes 12)?