Answer: 5 hours and 20 minutes.
Step-by-step explanation:
Let be "x" the time in hours that will take to paint [tex]\frac{2}{3}[/tex] of the room.
You know that 8 hours is the time it takes to paint the room.
With this information you can set up the following proportion:
[tex]\frac{8}{1}=\frac{x}{\frac{2}{3}}[/tex]
Finally, you must solve for the variable "x" in order to find its value.
You get that this is:
[tex]\frac{8}{1}=\frac{x}{\frac{2}{3}}\\\\\frac{8}{1}=\frac{3x}{2}\\\\(2)(8)=3x\\\\x=\frac{16}{3}\\\\x=5.33[/tex]
Since:
[tex]1\ hr=60\ min[/tex]
You can determine that:
[tex](0.33 hr)(\frac{60\ min}{1\ hr})=20\ min[/tex]
Then, the answer is: 5 hours and 20 minutes.
