Question

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.

Answer 1

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

$\dfrac{1}{6}+\dfrac{1}{4}+\dfrac{1}{t}=\dfrac{1}{2}$

i.e.  $\dfrac{1}{t}=\dfrac{1}{2}-(\dfrac{1}{6}+\dfrac{1}{4})$

i.e.  $\dfrac{1}{t}=\dfrac{1}{2}-(\dfrac{4+6}{24})$

i.e.  $\dfrac{1}{t}=\dfrac{1}{2}-\dfrac{10}{24}$

i.e.  $\dfrac{1}{t}=\dfrac{1}{2}-\dfrac{5}{12}$

i.e.  $\dfrac{1}{t}=\dfrac{6-5}{12}$

i.e.  $\dfrac{1}{t}=\dfrac{1}{12}$

i.e. t= 12

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