Answer:
2.22 hours
Explanation:
If Sally can paint the office by herself in 5 hours, we can say that in one hour she paints 1/5 of the office.
On the other hand, Lucy paints the office in 4 hours, which means that, in 1 hour she paints 1/4 of the office.
Therefore, to know how much they would paint per hour working together, we are going to sum up the fractions they paint per hour:
[tex]\frac{1}{5} +\frac{1}{4}=\frac{4+5}{20} =\frac{9}{20}[/tex]
Therefore, working together they will paint [tex]\frac{9}{20}[/tex] [tex]=0.45[/tex] of the office in one hour.
Now we can establish a rule of three: if they paint 0.45 of the office in 1 hour, how long (x) will it take them to paint 1.0 of the office?
[tex]1- 0.45\\x-1[/tex]
And therefore [tex]x = \frac{1}{0.45}=2.22[/tex]
Therefore, it will take them 2.22 hours to paint the office working together.
