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Question 388002: 1. My husband is a terrific cleaner. If he cleans the living room, it takes him 2 hours and 5
minutes. If I help, we can do the job in 1 hour and 20 minutes. How long does it take for
me to do it by myself?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! Rate * Time = Units Produced
R*T=U
The number of units produced is 1 clean house.
U = 1
Working together, the rate of each individual is additive.
R1 = his rate
R2 = your rate
(R1 + R2) * T = 1
He takes 2 hours and 5 minutes to clean the house by himself.
5 minutes = 5/60 hours = 1/12 hours = .0833333333 hours.
He take 2.083333333 hours to clean the house by himself.
Working by himself, the formula becomes R1*T = U which becomes:
R1*2.08333333 = 1
Divide both sides of this equation by 2.0833333, and you get:
R1 = 1.2.0833333 = .48
his rate is equal to .48 of the house in 1 hour.
The formula for both of you cleaning the house together becomes:
(.48 + R2) * T = 1
The time it takes both of you to clean the house is 1 hours and 20 minutes.
20 minutes = 20/60 hours = .3333333 hours.
The time it takes both of you to clean the house is 1.3333333 hours.
The formula becomes:
(.48 + R2) * 1.3333333 = 1
Remove parentheses to get:
.48 * 1.33333 + R2 * 1.3333333 = 1
Simplify to get:
.64 + R2 * 1.3333333 = 1
Subtract .64 from both sides of the equation and then divide both sides of the equation by 1.3333333 to get:
R2 = (1 - .64) / 1.3333333
Simplify to get:
R2 = .36 / 1.3333333 which becomes:
R2 = .27
Your rate of cleaning the house is equal to .27 of the house in 1 hour.
The formula for both of you completing the house at the same time becomes:
(.48 + .27) * 1.33333333 = 1
Simplify this to get:
.75 * 1.3333333 = 1
Simplify further to get:
1 = 1
The formula is good.
You can clean .27 of the house in 1 hour.
The formula for you working alone becomes:
R2 * T = 1
Since R2 = .27, this becomes:
.27 * T = 1
Divide both sides of this equation by .27 to get:
T = 3.703703704 house.
You would take 3.703703704 hours to clean the house by yourself.
.703703704 hours * 60 = 42.222222 minutes.
If would take approximately 3 hours and 42 minutes for you to clean the house by yourself at that rate.
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