document.write( "Question 488292: Please help me solve this word problem, I do not understand what to do.\r
\n" ); document.write( "\n" ); document.write( "It takes John 30 minutes to clean his house, When his wife helps him, it only takes him 18 minutes. How long would it take his wife by herself? \n" ); document.write( "
Algebra.Com's Answer #333336 by Theo(13342)\"\" \"About 
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rate * time = units of work
\n" ); document.write( "the unit of work is equal to 1 which is the house.
\n" ); document.write( "john takes 30 minutes to clean the house.
\n" ); document.write( "if time is in minutes, then the equation for john is:
\n" ); document.write( "rate * 30 = 1
\n" ); document.write( "divide both sides of this equation by 30 and you get:
\n" ); document.write( "rate = 1/30
\n" ); document.write( "this means that john can clean 1/30 of the house in 1 minute.
\n" ); document.write( "when john's wife helps him, they both can clean the house in 18 minutes.
\n" ); document.write( "rate * time = units of work.
\n" ); document.write( "the unit of work is still the house so it is equal to 1
\n" ); document.write( "the rate of work is the combined rate of john and his wife.
\n" ); document.write( "the time is takes is now 18 minutes.
\n" ); document.write( "the formula of rate * time becomes:
\n" ); document.write( "(john's rate + john's wife's rate) * 18 = 1
\n" ); document.write( "we know john's rate because we just solved for it.
\n" ); document.write( "we'll make john's wife's rate = x
\n" ); document.write( "our formula becomes:
\n" ); document.write( "(1/30 + x) * 18 = 1
\n" ); document.write( "we multiply this out to get:
\n" ); document.write( "18/30 + 18x = 1
\n" ); document.write( "we subtract 18/30 from both sides of this equation to get:
\n" ); document.write( "18x = 1 - 18/30
\n" ); document.write( "we simplify this to get:
\n" ); document.write( "18x = 12/30
\n" ); document.write( "we divide both sides of this equation by 18 to get:
\n" ); document.write( "x = (12/30) / 18 = 1/45
\n" ); document.write( "this means that john's wife's rate is equal to 1/45.
\n" ); document.write( "john's rate is 1/30 of the house in one minute.
\n" ); document.write( "john's wife's rate is 1/45 of the house in one minute.
\n" ); document.write( "i believe we will see that it will take john's wife 45 minutes to clean the hours by herself.
\n" ); document.write( "the formula is rate * time = units of work.
\n" ); document.write( "the units of work is still equal to 1.
\n" ); document.write( "the wife's rate is equal to 1/45.
\n" ); document.write( "the formula becomes:
\n" ); document.write( "1/45 * time = 1
\n" ); document.write( "multiply both sides of this equation by 45 to get:
\n" ); document.write( "time = 45 minutes.
\n" ); document.write( "when they work together, their rates are additive.
\n" ); document.write( "the formula becomes:
\n" ); document.write( "(1/30 + 1/45) * time = 1
\n" ); document.write( "this simplifies to:
\n" ); document.write( "(3/90 + 2/90) * time = 1 which simplifies further to:
\n" ); document.write( "5/90 * time = 1 which simplifies further to:
\n" ); document.write( "1/18 * time = 1
\n" ); document.write( "multiply both sides of this equation by 18 to get:
\n" ); document.write( "time = 18
\n" ); document.write( "the number work out ok so we have the answer.
\n" ); document.write( "the answer is:
\n" ); document.write( "john's wife takes 45 minutes to clean the house by herself.\r
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