This is about sanding and painting a boat's hull. Now that you have the sail figured out, it’s time to focus on the hull of the boat. You know the boat needs to be sanded first then painted. You own an electric sander so you will handle that part on your own. You definitely want help with the painting. Two of your cousins, Joe and Frances, have already committed to helping you with the painting. You have memories of helping your grandparents paint rooms in their home one summer. Joe and Frances were there and helped out with the painting. You want to get an idea of how long it will take to paint the hull. When working alone, Joe painted a room in six hours. Frances painted a room in four hours. You remember taking half the day to paint a room. The rooms were close enough to the same size.

Write a rational expression that models the three of you working together. (6 points)

If these times are approximately the same as painting the boat, write and solve a rational equation to determine how many hours it will take the three of you to paint the boat. (10 points)

You recall Joe hurting his wrist the summer you helped paint the rooms in your grandparents’ home. After his injury, he painted a room in 15 hours. Frances worked a little slower too. It took him five hours to paint a room. You don’t remember how long it took you to paint a room after Joe hurt his wrist, but you do recall the three of you painting a room in three hours. Write and solve a rational equation to determine how many hours it took you to paint a room after Joe’s injury. (16 points)

As long as no one is injured, another cousin JoAnna says she can help you, Joe, and Frances paint the boat in 45 minutes. If JoAnna were to paint the boat alone, how long would it take her? (18 points)