Answer: B. 9.9 hours
Step-by-step explanation:
Given : Paul can install a 300-square-foot hardwood floor in 18 hours.
We consider whole job as 1.
Rate of work per hour for Paul = [tex]r_1=\dfrac{1}{18}[/tex]
Matt can install the same floor in 22 hours.
Rate of work per hour for Matt = [tex]r_2=\dfrac{1}{22}[/tex]
Now , when they both work together , the rate of work = [tex]r=\dfrac{1}{t}[/tex] , where t is time taken by both together.
Since , [tex]r=r_1+r_2[/tex]
[tex]\dfrac{1}{t}=\dfrac{1}{18}+\dfrac{1}{22}[/tex]
[tex]\dfrac{1}{t}=\dfrac{11+9}{198}=\dfrac{20}{198}=\dfrac{10}{99}\\\\\Rightarrow\ t=\dfrac{99}{10}=9.9[/tex]
Hence, it would take 9.9 hours to install the floor working together.
Therefore , the correct answer is B. 9.9 hours .
