Question

Kalon and his friend Marna own a chimney sweep service company. Working together, they can clean a chimney in 1 5/7 hours. If it takes Kalon 4 hours to clean a 20-foot chimney by himself, how long does it take Marna to clean the same size chimney by herself?

Answer 1

It takes 3 hours for Marna to clean the same size chimney by herself.

Explanation:

Kalon and his friend Marna can clean a chimney in
`1 (5)/(7)= (12)/(7)`hours

They can do a part of work in 1 hour =
`(1)/((12)/(7)) = (7)/(12)`

Kalon can complete work in 4 hours

He can do a part of work in 1 hour =
`(1)/(4)`

So, Marna can do a part of work in 1 hour =
`(7)/(12)-(1)/(4)`

=
`(1)/(3)`

So, Marna can
`(1)/(3)` part of work in hour = 1

Marna can complete work in hour = 3

Hence it takes 3 hours for Marna to clean the same size chimney by herself.

Answer 2

The amount of work done by Kalon in an hour is equal to 1/4. This is based on his time to finish the job. Letting x be the number of hours Marna can finish the job alone will let her finish 1/x of the job in an hour. If their rates are added together and multiplied by the number of hours they worked together, the product should be one whole job.
(1/4 + 1/x)(1 5/7) = 1
The value of x is 3. Therefore, it will take 3 hours for Marna to clean the chimney alone.