document.write( "Question 388002: 1. My husband is a terrific cleaner. If he cleans the living room, it takes him 2 hours and 5
\n" ); document.write( "minutes. If I help, we can do the job in 1 hour and 20 minutes. How long does it take for
\n" ); document.write( "me to do it by myself?
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Algebra.Com's Answer #274293 by Theo(13342)\"\" \"About 
You can put this solution on YOUR website!
Rate * Time = Units Produced
\n" ); document.write( "R*T=U
\n" ); document.write( "The number of units produced is 1 clean house.
\n" ); document.write( "U = 1
\n" ); document.write( "Working together, the rate of each individual is additive.
\n" ); document.write( "R1 = his rate
\n" ); document.write( "R2 = your rate
\n" ); document.write( "(R1 + R2) * T = 1
\n" ); document.write( "He takes 2 hours and 5 minutes to clean the house by himself.
\n" ); document.write( "5 minutes = 5/60 hours = 1/12 hours = .0833333333 hours.
\n" ); document.write( "He take 2.083333333 hours to clean the house by himself.
\n" ); document.write( "Working by himself, the formula becomes R1*T = U which becomes:
\n" ); document.write( "R1*2.08333333 = 1
\n" ); document.write( "Divide both sides of this equation by 2.0833333, and you get:
\n" ); document.write( "R1 = 1.2.0833333 = .48
\n" ); document.write( "his rate is equal to .48 of the house in 1 hour.
\n" ); document.write( "The formula for both of you cleaning the house together becomes:
\n" ); document.write( "(.48 + R2) * T = 1
\n" ); document.write( "The time it takes both of you to clean the house is 1 hours and 20 minutes.
\n" ); document.write( "20 minutes = 20/60 hours = .3333333 hours.
\n" ); document.write( "The time it takes both of you to clean the house is 1.3333333 hours.
\n" ); document.write( "The formula becomes:
\n" ); document.write( "(.48 + R2) * 1.3333333 = 1
\n" ); document.write( "Remove parentheses to get:
\n" ); document.write( ".48 * 1.33333 + R2 * 1.3333333 = 1
\n" ); document.write( "Simplify to get:
\n" ); document.write( ".64 + R2 * 1.3333333 = 1
\n" ); document.write( "Subtract .64 from both sides of the equation and then divide both sides of the equation by 1.3333333 to get:
\n" ); document.write( "R2 = (1 - .64) / 1.3333333
\n" ); document.write( "Simplify to get:
\n" ); document.write( "R2 = .36 / 1.3333333 which becomes:
\n" ); document.write( "R2 = .27
\n" ); document.write( "Your rate of cleaning the house is equal to .27 of the house in 1 hour.
\n" ); document.write( "The formula for both of you completing the house at the same time becomes:
\n" ); document.write( "(.48 + .27) * 1.33333333 = 1
\n" ); document.write( "Simplify this to get:
\n" ); document.write( ".75 * 1.3333333 = 1
\n" ); document.write( "Simplify further to get:
\n" ); document.write( "1 = 1
\n" ); document.write( "The formula is good.
\n" ); document.write( "You can clean .27 of the house in 1 hour.
\n" ); document.write( "The formula for you working alone becomes:
\n" ); document.write( "R2 * T = 1
\n" ); document.write( "Since R2 = .27, this becomes:
\n" ); document.write( ".27 * T = 1
\n" ); document.write( "Divide both sides of this equation by .27 to get:
\n" ); document.write( "T = 3.703703704 house.
\n" ); document.write( "You would take 3.703703704 hours to clean the house by yourself.
\n" ); document.write( ".703703704 hours * 60 = 42.222222 minutes.
\n" ); document.write( "If would take approximately 3 hours and 42 minutes for you to clean the house by yourself at that rate.\r
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