Answer: 7.8 days
Step-by-step explanation:
Painter can get the job done in 15 days so gets [tex]\dfrac{1}{15}[/tex] of the job done in 1 day.
Coworker can get the job done in 10 days so gets [tex]\dfrac{1}{10}[/tex] of the job done in 1 day.
Together, they get [tex]\dfrac{1}{15}+\dfrac{1}{10}[/tex] of the job done in 1 day.
Painter worked for 3 days so completed [tex]\dfrac{1}{15}(3)=\dfrac{1}{5}[/tex] of the job.
That leaves a remaining of [tex]1-\dfrac{1}{5}=\dfrac{4}{5}[/tex] of the job to be completed.
Let x represent the number of days it will take them to work together.
Painter + Coworker = Together
[tex]\dfrac{1}{15}(x)\quad +\quad \dfrac{1}{10}(x)\quad =\quad \dfrac{4}{5}[/tex]
Multiply by 30 to eliminate the denominator:
[tex]\dfrac{1}{15}(x)(30) +\ \dfrac{1}{10}(x)(30) = \dfrac{4}{5}(30)[/tex]
Simplify and solve for x:
2x + 3x = 24
5x = 24
[tex]x=\dfrac{24}{5}[/tex]
x = 4.8
Remember that Painter worked 3 days alone in addition to the 4.8 days they worked together.
So the total time to paint the building is 3 + 4.8 = 7.8
