document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=439251>Question 439251</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A day laborer takes three more days to paint a house than an apprentice painter. A master painter takes three days fewer than the apprentice.  The master painter can do as much work in seven days as the day laborer and the apprentice working together can accomplish in six days.  How long would it take the apprentice alone to paint the house? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #303533 by </B><A HREF=/tutors/aboutme.mpl?userid=ptaylor><B>ptaylor(2198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ptaylor><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=ptaylor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=303533\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x=amount of time it takes the apprentice to paint the house<BR>\n" );
document.write( "Then the apprentice paints at the rate of 1/x house per day<BR>\n" );
document.write( "x+3=amount of time needed by the day laborer to paint the house<BR>\n" );
document.write( "Then the day laborer works at the rate of 1/(x+3) house per day<BR>\n" );
document.write( "x-3=amount of time needed by the master painter to paint the house<BR>\n" );
document.write( "Then the master painter works at the rate of 1/(x-3) house per day<BR>\n" );
document.write( "In 7 days the master painter can paint 7/(x-3) of the house<BR>\n" );
document.write( "In 6 days the apprentice can paint 6/x house<BR>\n" );
document.write( "In 6 days the day laborer can paint 6/(x+3) house <BR>\n" );
document.write( "Together the day laborer and the apprentice can paint (6/x + 6/(x+3)) house\r<BR>\n" );
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document.write( "Now we are told that 7/(x-3)=6/x + 6/(x+3) multiply each term by x(x-3)(x+3)<BR>\n" );
document.write( "7x(x+3)=6(x-3)(x+3)+6x(x-3) expand<BR>\n" );
document.write( "7x^2+21x=6x^2-54 + 6x^2-18x subtract 7x^2 and also 21x from both sides<BR>\n" );
document.write( "0=6x^2-7x^2-21x-54+6x^2-18x or<BR>\n" );
document.write( "5x^2-39x-54=0 ---quadratic in standard form<BR>\n" );
document.write( "When we solve this quadratic we get:<BR>\n" );
document.write( "x=(39+-51)/10<BR>\n" );
document.write( "x=-1.2----no good--- can't have negative times<BR>\n" );
document.write( "and<BR>\n" );
document.write( "x=9----so it takes the apprentice 9 hours to paint the house working alone<BR>\n" );
document.write( "It takes the day laborer x+3=9+3=12 hours<BR>\n" );
document.write( "And it takes the master painter x-3=9-3=6 hours\r<BR>\n" );
document.write( "\n" );
document.write( "CK<BR>\n" );
document.write( "In 7 hours the master painter can paint 7/6 house <BR>\n" );
document.write( "In 6 hours the apprentice can paint 6/9 house<BR>\n" );
document.write( "And in 6 hours the day laborer can paint 6/12 house<BR>\n" );
document.write( "Does 6/9  + 6/12 = 7/6 ??<BR>\n" );
document.write( "24/36 + 18/36 = 42/36<BR>\n" );
document.write( "42/36=42/36<BR>\n" );
document.write( "7/6=7/6\r<BR>\n" );
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document.write( "Hope this helps----ptaylor<BR>\n" );
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