document.write( "Question 199036This question is from textbook algebra and trigonometry
\n" ); document.write( ": Betty and karen have been hired to paint the houses in a new development. Working together the women can paint a house in two thirds the time that it takes karen working alone. Betty takes 6 hours to paint a house alone. How long does it take karen to paint a house working alone? \n" ); document.write( "
Algebra.Com's Answer #149519 by nerdybill(7384)\"\" \"About 
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Betty and karen have been hired to paint the houses in a new development. Working together the women can paint a house in two thirds the time that it takes karen working alone. Betty takes 6 hours to paint a house alone. How long does it take karen to paint a house working alone?
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\n" ); document.write( "Let k = time it takes Karen to paint the house alone
\n" ); document.write( "then
\n" ); document.write( "(2/3)(k)(1/k + 1/6) = 1
\n" ); document.write( "(2k/3)(1/k + 1/6) = 1
\n" ); document.write( "(2k)(1/k + 1/6) = 3
\n" ); document.write( "(2 + k/3) = 3
\n" ); document.write( "Multiplying both sides by 3:
\n" ); document.write( "6 + k = 9
\n" ); document.write( "k = 3 hours\r
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