Answer:
Required equation : [tex]\frac{1}{t}=\frac{1}{3}+\frac{1}{9}[/tex]
Together they can paint the same room in 2.25 hours or 2 hours 15 minutes.
Step-by-step explanation:
It is given that Dale Horton can paint a certain room in 3 hours.
One hour woks of Dale Horton = 1/3
Kathy Garcia can paint the same room in 9 hours.
One hour woks of Kathy Garcia = 1/9
Let together they can paint the same room in t hours.
One hour woks of both = 1/t
[tex]\frac{1}{t}=\frac{1}{3}+\frac{1}{9}[/tex]
[tex]\frac{1}{t}=\frac{3+1}{9}[/tex]
[tex]\frac{1}{t}=\frac{4}{9}[/tex]
After reciprocal we get
[tex]\frac{t}{1}=\frac{9}{4}[/tex]
[tex]t=2.25[/tex]
1 hour = 60 minutes.
0.25 hour = 15 minutes.
Therefore, together they can paint the same room in 2.25 hours or 2 hours 15 minutes.
