Question

Kalon and his friend Marna own a chimney sweep service company. Working together, they can clean a 20-foot chimney in 1Five-sevenths 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?


Rate
(Chimneys per Hour)
Time
(Hours)
Fraction Completed
Kalon
One-fourth
1 and five-sevenths
Three-sevenths
Marna
x
1 and five-sevenths
StartFraction 12 x Over 7 EndFraction
3 hours
4 hours
5 hours
6 and six-sevenths hours

Answer 1

Kalon's rate = 1/4 chimney per hour. Together they finish in 1 5/7 = 12/7 hours, so combined rate = 1 ÷ (12/7) = 7/12 chimney per hour.

Marna's rate = (combined) − (Kalon) = 7/12 − 1/4 = 7/12 − 3/12 = 4/12 = 1/3.

Thus Marna takes 3 hours to clean the chimney by herself.