document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=347067>Question 347067</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a mason can build a wall in 6 hours less than an apprentive. together they can build the wall in 4 hours. how long would it take the apprentice, working alone, to build the wall? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #248152 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=248152\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x=amount of time it takes the apprentice working alone to build the wall<BR>\n" );
document.write( "Then the apprentice works at the rate of 1/x wall per hour<BR>\n" );
document.write( "And x-6=amount of time it takes the mason to build the wall<BR>\n" );
document.write( "Then the mason works at the rate of 1/(x-6) wall per hour<BR>\n" );
document.write( "Together the mason and apprentice works at the rate of 1/4 wall per hour<BR>\n" );
document.write( "So our equation to solve is:<BR>\n" );
document.write( "1/x + 1/(x-6)=1/4 multiply each term by 4x(x-6)<BR>\n" );
document.write( "4(x-6)+4x=x(x-6) get rid of parens<BR>\n" );
document.write( "4x-24+4x=x^2-6x or<BR>\n" );
document.write( "8x-24=x^2-6x subtract 8x from and add 24 to both sides<BR>\n" );
document.write( "x^2-6x-8x+24=0<BR>\n" );
document.write( "x^2-14x+24=0 ----quadratic in standard form and it can be factored<BR>\n" );
document.write( "(x-2)(x-12)=0<BR>\n" );
document.write( "x=2 hrs----THIS CANNOT BE A SOLUTION; THE MASON CANNOT WORK 6 HRS LESS THAN 2 HOURS ---CANNOT HAVE NEGATIVE TIMES IN THIS CASE<BR>\n" );
document.write( "x=12 hrs----time it takes apprentice working alone<BR>\n" );
document.write( "Then mason takes 6 hrs working alone to build the wall\r<BR>\n" );
document.write( "\n" );
document.write( "CK<BR>\n" );
document.write( "1/12 + 1/6=1/4<BR>\n" );
document.write( "3/12=1/4<BR>\n" );
document.write( "1/4=1/4\r<BR>\n" );
document.write( "\n" );
document.write( "Hope this helps---ptaylor </SPAN>\n" );
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