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
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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
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
