Answer:
The time it takes Candy working alone to finish cleaning the house is 3 hours
The time it takes Cindy working alone to finish cleaning the house is 6 hours
Step-by-step explanation:
The given parameters are;
The time it takes Cindy and Candy to finish cleaning the house = 2 hrs
The time it takes Cindy working alone to finish cleaning the house = 3 hrs + The time it takes Candy working alone to finish cleaning the house
Let x represent the time in hours, it takes Candy working alone to finish cleaning the house
∴ The time, in hours, it takes Cindy working alone to finish cleaning the house = 3 + x
2/x + 2/(3 + x) = 1
(2·(3 + x) + 2·x)/x·(3 + x) = 1
(2·(3 + x) + 2·x) = x·(3 + x)
6 + 2·x + 2·x = 3·x + x²
6 + 4·x = 3·x + x²
x² + 3·x - 4·x - 6 = 0
x² - x - 6 = 0
(x - 3)·(x + 2) = 0
x = 3, or x = -2
Therefore, it takes Candy, x = 3 hours working alone to finish cleaning the house, and it takes Cindy 3 + x = 3 + 3 = 6 hours working alone to finish cleaning the house.
The time it takes Candy working alone to finish cleaning the house = 3 hours
The time it takes Cindy working alone to finish cleaning the house = 6 hours
