Problema Solution
Sally can clean the house in 6 hours, her father can clean the house in 4 hours, and her younger brother, Dennis, can completely mess up the house in 8 hours. If Sally and her father clean and Dennis plays, how long will it take to clean the house?
Answer provided by our tutors
Let 'x' represent the hours needed to clean the house when Sally and her father are cleaning together and her brother Dennis is playing at the same time.
In 1 hour Sally will clean 1/6 of the house.
In 1 hour Sally's father will clean 1/4 of the house.
In 1 hour Dennis will mess up 1/8 of the house.
Now we can write the following equation:
1/6 + 1/4 - 1/8 = 1/x
........
click here to see the equation solved for x
........
x = 24/7 hr
x = 3 hr 17 min
It will take 3 hours and 17 minutes to clean the house.