Answer:
Alicia will take 5 hours to clean the barn.
Step-by-step explanation:
John and Alicia are asked to clean the barn.
John can clean the barn alone in 3 hours.
So work done in one hour = [tex]\frac{1}{3}[/tex]
Let Alicia takes x hours to clean the barn alone so work done in one hour by Alicia = [tex]\frac{1}{x}[/tex]
Now it is given in the question that together they can clean the barn in [tex]1\frac{7}{8}[/tex] hour or [tex]\frac{15}{8}[/tex] hours.
So work done together in one hour = [tex]\frac{1}{\frac{15}{8} }=\frac{8}{15}[/tex]
Now we know work done in one hour by John + work done in one hour by Alicia = work done in one hour by both.
[tex]\frac{1}{x}+\frac{1}{3}=\frac{8}{15}[/tex]
[tex]\frac{3+x}{3x}=\frac{8}{15}[/tex]
15(3+x) = 8 (3x) [By cross multiplication]
45 + 15x = 24x - 15x
45 = 9x
x = [tex]\frac{45}{9}[/tex] = 5
Therefore, Alicia will take 5 hours to clean the barn by herself.
