document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=128173>Question 128173</A>: <I><SPAN STYLE=\"word-break: break-all;\"> It takes Tom 3 hours less to paint a fence than Jim. If the two boys work together, they can paint the fence in 2 hours. How many hours would each boy, working alone, need to paint the fence? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #93852 by </B><A HREF=/tutors/aboutme.mpl?userid=marcsam823><B>marcsam823(57)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=marcsam823><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=93852\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. Set up the variables:<BR>\n" );
document.write( "Let x = # hours it takes Jim to paint the fence alone<BR>\n" );
document.write( "Let x - 3 = # hours it takes Tom to paint the fence alone<BR>\n" );
document.write( "Let 1/x = amount of the fence painted by Jim in 1 hour<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28x+-+3%29 ALIGN=MIDDLE  ALT=\"1%2F%28x+-+3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = amount of the fence painted by Tom in 1 hour\r<BR>\n" );
document.write( "\n" );
document.write( "2. Set up the equation(s)<BR>\n" );
document.write( "In 1 hour the two boys paint <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fx+%2B+1%2F%28x-3%29 ALIGN=MIDDLE  ALT=\"1%2Fx+%2B+1%2F%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the fence\r<BR>\n" );
document.write( "\n" );
document.write( "In 2 hours the two boys paint:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2=+1 ALIGN=MIDDLE  ALT=\"2=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >  (1 = 1 job or 100% of the job)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Fx+%2B+2%2F%28x-3%29=+1 ALIGN=MIDDLE  ALT=\"2%2Fx+%2B+2%2F%28x-3%29=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "3. Find the common denominator:  (x)(x-3)= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+3x ALIGN=MIDDLE  ALT=\"x%5E2+-+3x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A%28x-3%29%2F%28x%5E2+-+3x%29%2B+2%28x%29%2F%28x%5E2+-+3x%29+=+%28x%5E2+-+3x%29%2F%28x%5E2+-+3x%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "4. Multiply both sides of the equation by (x^2 - 3x):<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28x-3%29+%2B+2x+=+x%5E2+-+3x ALIGN=MIDDLE  ALT=\"2%28x-3%29+%2B+2x+=+x%5E2+-+3x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "5. Combine like terms:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x+-+6++%2B+2x+=+x%5E2+-+3x ALIGN=MIDDLE  ALT=\"2x+-+6++%2B+2x+=+x%5E2+-+3x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x+-+6+=+x%5E2+-+3x ALIGN=MIDDLE  ALT=\"4x+-+6+=+x%5E2+-+3x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+x%5E2+-+7x+%2B+6 ALIGN=MIDDLE  ALT=\"0+=+x%5E2+-+7x+%2B+6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "6. Factor and solve for x:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+1%29%28x+-+6%29+=+0 ALIGN=MIDDLE  ALT=\"%28x+-+1%29%28x+-+6%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+1 ALIGN=MIDDLE  ALT=\"x+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+6 ALIGN=MIDDLE  ALT=\"x+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since we have two answers we need to see which one makes sense by plugging each into our equations:<BR>\n" );
document.write( "Jim can paint a fence in x = 1 hours<BR>\n" );
document.write( "Tom can paint a fence in x-3 = -2 hours<BR>\n" );
document.write( "We must reject this answer because time can never be a negative value.<BR>\n" );
document.write( "Substitute x = 6:<BR>\n" );
document.write( "Jim can paint the fence in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+6 ALIGN=MIDDLE  ALT=\"x+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" > hours<BR>\n" );
document.write( "Tom can paint the fence in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+-+3+=+6+-+3+=+3 ALIGN=MIDDLE  ALT=\"x+-+3+=+6+-+3+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" > hours<BR>\n" );
document.write( "This is the answer we are looking for.\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );