Question 887380
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?
***
let x= how long will it take to clean the house
1/6=Sally's work rate
1/4=father's work rate
-1/8=Dennis' work rate
1/x=work rate working together
sum of indv. work rates=work rate working together
..
{{{1/6+1/4-1/8=1/x}}}
lcd:24
{{{4+6-3=24/x}}}
7=24/x
x=24/7
how long will it take to clean the house=24/7 hrs