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 cl

Question 438028: 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?
Found 2 solutions by ankor@dixie-net.com, Edwin McCravy:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
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?
:
Let t = time required when all three are involved
:
Clean is positive
Messing = negative, obviously
:
Let a cleaned house = 1
:
+ - = 1
Multiply by 24
24* + 24* - 24* = 24(1)
Cancel the denominators, results:
4t + 6t - 3t = 24
:
7t = 24
t =
t = 3 hrs which is 3 + *60 = 3 hrs 25.7 min
Answer by Edwin McCravy(20054) (Show Source): You can put this solution on YOUR website!
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

Make this chart: no. of houses cleaned | time | rate in houses/hour -------------------------------------------------------------- Sally | | Father | | Dennis | | -------------------------------------------------------------- All 3 | | Let x be the time for all three doing their thing, whether cleaning or playing, to get 1 house clean. So we put x for the time for all 3: no. of houses cleaned | time | rate in houses/hour -------------------------------------------------------------- Sally | | Father | | Dennis | | -------------------------------------------------------------- All 3 | x | Now fill in the 3 times: no. of houses cleaned | time | rate in houses/hour -------------------------------------------------------------- Sally | 6 | Father | 4 | Dennis | 8 | -------------------------------------------------------------- All 3 | x | Sally can clean 1 house in 6 hours, so we put 1 for the no. of houses Sally can clean. Her father can clean 1 house in 4 hours, so we put 1 for the no. of houses her father can clean. Dennis can mess up 1 house in 8 hours, so we put -1 for the no. of houses Dennis can clean, because to mess up 1 house is mathematically the same as "cleaning -1 house" Since all 3 will be cleaning 1 house, put 1 for the no. of houses cleaned by all 3 no. of houses cleaned | time | rate in houses/hour -------------------------------------------------------------- Sally 1 | 6 | Father 1 | 4 | Dennis -1 | 8 | -------------------------------------------------------------- All 3 1 | x | Fill in the rates in houses/hour by dividing the no. of houses by the number of hours: no. of houses cleaned | time | rate in houses/hour -------------------------------------------------------------- Sally 1 | 6 | 1/6 Father 1 | 4 | 1/4 Dennis -1 | 8 | -1/8 -------------------------------------------------------------- All 3 1 | x | 1/x Now the equation come from Sally's rate + Father's rate + Dennis' rate = Rate for all 3 1/6 + 1/4 - 1/8 = 1/x Clear of fractions by multiplying through by LCD of 24x 4x + 6x - 3x = 24 7x = 24 x = 24/7 = 3 3/7 hours Edwin

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