cindy and candy are task to clean their house cindy and candy can finish cleaning the house in 2hrs if it takes cindy working alone 3hrs longer than it takes candy working alone how many hours will each finish working

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