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

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

Answer 2

Alicia will take 5 hours to clean the barn.

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 =
`(1)/(3)`

Let Alicia takes x hours to clean the barn alone so work done in one hour by Alicia =
`(1)/(x)`

Now it is given in the question that together they can clean the barn in
`1(7)/(8)` hour or
`(15)/(8)` hours.

So work done together in one hour =
`(1)/((15)/(8) )=(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.

`(1)/(x)+(1)/(3)=(8)/(15)`

`(3+x)/(3x)=(8)/(15)`

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

45 + 15x = 24x - 15x

45 = 9x

x =
`(45)/(9)` = 5

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