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. determine how long it would take francisco to paint one room on his own.

 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

i.e.  

i.e.  

i.e.  

i.e.  

i.e.  

i.e.  

i.e. t= 12

Hence,  Francisco would take 12 hours to  paint one room on his own.