Answer: 12 hours
Step-by-step explanation:
Given : Working together, it takes Sam, Jenna, and Francisco two hours to paint one room.
When Sam works alone, he can paint one room in 6 hours. When Jenna works alone, she can paint one room in 4 hours.
Let 't' be the time taken by Francisco to paint one room on his own.
Then , we have
Rate of work of Sam +Rate of work of Jenna + Rate of work of Francisco =Rate of work they all do together
[tex]\dfrac{1}{6}+\dfrac{1}{4}+\dfrac{1}{t}=\dfrac{1}{2}[/tex]
i.e. [tex]\dfrac{1}{t}=\dfrac{1}{2}-(\dfrac{1}{6}+\dfrac{1}{4})[/tex]
i.e. [tex]\dfrac{1}{t}=\dfrac{1}{2}-(\dfrac{4+6}{24})[/tex]
i.e. [tex]\dfrac{1}{t}=\dfrac{1}{2}-\dfrac{10}{24}[/tex]
i.e. [tex]\dfrac{1}{t}=\dfrac{1}{2}-\dfrac{5}{12}[/tex]
i.e. [tex]\dfrac{1}{t}=\dfrac{6-5}{12}[/tex]
i.e. [tex]\dfrac{1}{t}=\dfrac{1}{12}[/tex]
i.e. t= 12
Hence, Francisco would take 12 hours to paint one room on his own.
