Working together, shawn and hector can install a tile floor in 6 hours. it would take shawn 9 hours to do the job alone. what is the value of r, the part of the tile that hector could install in 1 hour?

First, let x be the number of hours it will take for Hector to finish the same job alone. This means that every hour, Hector can do 1/x of the job. The amount of work done by Shawn and Hector in 6 hours should be equal to 1 complete work. This can be expressed as,
                      (1/9 + 1/x)(6) = 1
The value of x is 18. Thus, Hector can to 1/18 of the job in one hour.