SOLUTION: Housecleaning: Sally can clean the house in 6 hours, and her father can clean the house in 4 hours. Sally's younger brother, Dennis, can completely mess up the house in 8 hours. If

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Question 1119779: Housecleaning: Sally can clean the house in 6 hours, and her father can clean the house in 4 hours. Sally's 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?
Found 3 solutions by josgarithmetic, ikleyn, Shin123:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Just a hint:
Sally and Father work at positive rates. Brother "works" at a negative rate. One job, 1 whole job, is "cleaning the house".

Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
.
Every hour, Sally makes 1%2F6 of the job;

            the father makes 1%2F4 of the job;

            and  small Dennis messes up 1%2F8 of the job.


So, their combined rate of work is  1%2F6+%2B+1%2F4+-+1%2F8 = 4%2F24+%2B+6%2F24+-+3%2F24 = 7%2F24 of the job per hour.


It means that they will complete cleaning in 24%2F7 hours = 33%2F7 hours (if they be able to neutralize Dennis at the end).

Solved.

-------------------
It is a typical and standard joint work problem.

There is a wide variety of similar solved joint-work problems with detailed explanations in this site.  See the lessons
    - Using Fractions to solve word problems on joint work
    - Solving more complicated word problems on joint work
    - Selected joint-work word problems from the archive


Read them and get be trained in solving joint-work problems.

Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this textbook under the topic
"Rate of work and joint work problems"  of the section  "Word problems".


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.


Answer by Shin123(626) About Me  (Show Source):
You can put this solution on YOUR website!
Sally can finish 1%2F6 of the job in a hour,her dad can finish 1%2F4 of the job in a hour, and Dennis can finish -%281%2F8%29 of the job in a hour. 1%2F6%2B1%2F4-1%2F8=4%2F24%2B6%2F24-3%2F24=7%2F24
1%2F%287%2F24%29=24%2F7 It will take them 3%263%2F7 hours to finish the job,if they can get Dennis to stop playing when they are finished.