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

Kalon + Marna = 12/7 hours working together
( I attached two formulas. Use formula 3)

Worker 2 Time = (worker 1 Time) * Total Time / [(worker 1 Time) - Total Time]
Worker 2 Time = ((4) * 12/7) / [4 - 12/7]
Worker 2 Time = 6.8571428571 / 2.2857142857
Worker 2 Time = 3 hours

Answer 2

Explanation:

Given that Kalon and his friend Marna own a chimney sweep service company. Working together, they can clean a chimney in 1 5/7 hours and it takes Kalon 4 hours to clean a 20-foot chimney by himself.

i.e. Kalon can do in one hour 1/4 of the work

Marna can do in one hour 1/x of the work

(assuming total x hours Marns taes to clean the same size chimney)

Together they clean

`(7)/(12)`

`(1)/(4) +(1)/(x) =(7)/(12)`

Simplify to get

`12(x+4)=28x\\3x+12=7x\\4x=12\\x=3`

Marna takes 3 hours to clean the same size chimney