Question

John and alicia are asked to clean the barn. john can clean the barn by himself in 3 hours and together they can clean the barn in 1 7/8 hours. how long would it take alicia to clean the barn by herself?

Answer 1

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 = $\frac{1}{3}$

Let Alicia takes x hours to clean the barn alone so work done in one hour by Alicia = $\frac{1}{x}$

Now it is given in the question that together they can clean the barn in $1\frac{7}{8}$ hour or $\frac{15}{8}$ hours.

So work done together in one hour = $\frac{1}{\frac{15}{8} }=\frac{8}{15}$

Now we know work done in one hour by John + work done in one hour by Alicia = work done in one hour by both.

$\frac{1}{x}+\frac{1}{3}=\frac{8}{15}$

$\frac{3+x}{3x}=\frac{8}{15}$

15(3+x) = 8 (3x) [By cross multiplication]

45 + 15x = 24x - 15x

45 = 9x

x = $\frac{45}{9}$ = 5

Therefore, Alicia will take 5 hours to clean the barn by herself.

Answer 2

1 and 1/8 of an hour because Alisha took away that amount of time from johns time.<span />