Answer: 8 hours
Step-by-step explanation:
Let x be the time taken by each person to paint the fence.
Given: Tom and Becky can paint Jim's fence together in 12 hours.
Since all people paint at the same rate, then we have the following equation ;-
[tex]\dfrac{1}{x}+\dfrac{1}{x}=\dfrac{1}{12}\\\\\Rightarrow\ \dfrac{2}{x}=\dfrac{1}{12}\\\\\Rightarrow\ x=24[/tex]
Thus, the time taken by each person to paint the fence alone = 24 hours
Now, the time taken by all three paint together:-
[tex]\dfrac{1}{t}=\dfrac{1}{24}+\dfrac{1}{24}+\dfrac{1}{24}\\\\\Rightarrow\ \dfrac{1}{t}=\dfrac{3}{24}\\\\\Rightarrow\ t=\dfrac{24}{3}=8\text{ hours}[/tex]
Hence, it would take 8 hours if all three paint together.
