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?

The product of the sum of the their rates and the time it took them to finish the job should be equal to one whole job. This may be expressed by the equation,

(1/9 + r) x 6 = 1

Solving for the value of r gives an answer of r = 1/18. Thus, Hector does 1/18 of the job in 1 hour.