Answer: Let's assume Hector's rate of work (r) is measured in parts per hour. Since we know that Shawn and Hector together can install the tile floor in 6 hours, we can set up an equation based on their rates of work.
Shawn's rate of work (s) is 1 job in 9 hours, so his rate is:
s = 1 job / 9 hours
Hector's rate of work (r) is the unknown we want to find.
Together, their combined rate of work (s + r) is 1 job in 6 hours:
s + r = 1 job / 6 hours
Now, we can solve for Hector's rate (r):
r = 1 job / 6 hours - s
Substitute the value of s:
r = 1 job / 6 hours - 1 job / 9 hours
To find a common denominator, which is 18, let's rewrite the fractions:
r = (3/18) - (2/18)
r = 1/18
So, Hector's rate of work (r) is 1 part per hour (or 1/18 job per hour).