document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1174769>Question 1174769</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Homer and Mike were replacing the boards on​ Mike's old deck. Mike can do the job alone in 1 hour less time than Homer. They worked together for 5 hours until Homer had to go home. Mike finished the job working by himself in an additional 2 hours. How long would it have taken Homer to fix the deck​ himself? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #800254 by </B><A HREF=/tutors/aboutme.mpl?userid=VFBundy><B>VFBundy(438)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=VFBundy><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=VFBundy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=800254\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Homer's rate of work = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fx ALIGN=MIDDLE  ALT=\"1%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the job per hour<BR>\n" );
document.write( "Mike's rate of work = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28x-1%29 ALIGN=MIDDLE  ALT=\"1%2F%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the job per hour<BR>\n" );
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document.write( "Rate of work working together = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fx ALIGN=MIDDLE  ALT=\"1%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28x-1%29 ALIGN=MIDDLE  ALT=\"1%2F%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the job per hour<BR>\n" );
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document.write( "Simplify:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%29%2F%28x%28x-1%29%29 ALIGN=MIDDLE  ALT=\"%28x-1%29%2F%28x%28x-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F%28x%28x-1%29%29 ALIGN=MIDDLE  ALT=\"x%2F%28x%28x-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<pr><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%2Bx%29%2F%28x%28x-1%29%29 ALIGN=MIDDLE  ALT=\"%28x-1%2Bx%29%2F%28x%28x-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<pr><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x-1%29%2F%28x%28x-1%29%29 ALIGN=MIDDLE  ALT=\"%282x-1%29%2F%28x%28x-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Rate of work working together = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x-1%29%2F%28x%28x-1%29%29 ALIGN=MIDDLE  ALT=\"%282x-1%29%2F%28x%28x-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the job per hour<BR>\n" );
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document.write( "After working five hours together, calculate the amount of the job that was completed:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5+%2A+%28%282x-1%29%2F%28x%28x-1%29%29%29 ALIGN=MIDDLE  ALT=\"5+%2A+%28%282x-1%29%2F%28x%28x-1%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<pr><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2810x+-+5%29%2F%28x%28x-1%29%29 ALIGN=MIDDLE  ALT=\"%2810x+-+5%29%2F%28x%28x-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Therefore, the amount of the job that is left to be completed is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-+%2810x+-+5%29%2F%28x%28x-1%29%29 ALIGN=MIDDLE  ALT=\"1-+%2810x+-+5%29%2F%28x%28x-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<pr><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%28x-1%29%29%2F%28x%28x-1%29%29+-+%2810x+-+5%29%2F%28x%28x-1%29%29 ALIGN=MIDDLE  ALT=\"%28x%28x-1%29%29%2F%28x%28x-1%29%29+-+%2810x+-+5%29%2F%28x%28x-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<pr><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2-x%29%2F%28x%28x-1%29%29+-+%2810x+-+5%29%2F%28x%28x-1%29%29 ALIGN=MIDDLE  ALT=\"%28x%5E2-x%29%2F%28x%28x-1%29%29+-+%2810x+-+5%29%2F%28x%28x-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<pr><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2+-+x+-+%2810x+-+5%29%29%2F%28x%28x-1%29%29 ALIGN=MIDDLE  ALT=\"%28x%5E2+-+x+-+%2810x+-+5%29%29%2F%28x%28x-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<pr><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2+-+x+-+10x+%2B+5%29%2F%28x%28x-1%29%29 ALIGN=MIDDLE  ALT=\"%28x%5E2+-+x+-+10x+%2B+5%29%2F%28x%28x-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<pr><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2+-+11x+%2B+5%29%2F%28x%28x-1%29%29 ALIGN=MIDDLE  ALT=\"%28x%5E2+-+11x+%2B+5%29%2F%28x%28x-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Mike finishes the job in two hours.  This means Mike's rate of work per hour is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >* <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2+-+11x+%2B+5%29%2F%28x%28x-1%29%29 ALIGN=MIDDLE  ALT=\"%28x%5E2+-+11x+%2B+5%29%2F%28x%28x-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<pr><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2+-+11x+%2B+5%29%2F%282x%28x-1%29%29 ALIGN=MIDDLE  ALT=\"%28x%5E2+-+11x+%2B+5%29%2F%282x%28x-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<pr><BR>\n" );
document.write( "So, Mike's rate of work is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2+-+11x+%2B+5%29%2F%282x%28x-1%29%29 ALIGN=MIDDLE  ALT=\"%28x%5E2+-+11x+%2B+5%29%2F%282x%28x-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the job per hour.<BR>\n" );
document.write( "<pr><BR>\n" );
document.write( "From earlier, we know that Mike's rate of work is also <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28x-1%29 ALIGN=MIDDLE  ALT=\"1%2F%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the job per hour.  Therefore:<BR>\n" );
document.write( "<pr><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2+-+11x+%2B+5%29%2F%282x%28x-1%29%29 ALIGN=MIDDLE  ALT=\"%28x%5E2+-+11x+%2B+5%29%2F%282x%28x-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28x-1%29 ALIGN=MIDDLE  ALT=\"1%2F%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Solve for x.<BR>\n" );
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document.write( "Cross-multiply:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%29%28x%5E2+-+11x+%2B+5%29 ALIGN=MIDDLE  ALT=\"%28x-1%29%28x%5E2+-+11x+%2B+5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%28x-1%29 ALIGN=MIDDLE  ALT=\"2x%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<pr><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2+-+11x+%2B+5%29 ALIGN=MIDDLE  ALT=\"%28x%5E2+-+11x+%2B+5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x ALIGN=MIDDLE  ALT=\"2x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<pr><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+13x+%2B+5 ALIGN=MIDDLE  ALT=\"x%5E2+-+13x+%2B+5\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Use the quadratic formula to solve for x:<BR>\n" );
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document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2813-sqrt%28149%29%29%2F2 ALIGN=MIDDLE  ALT=\"%2813-sqrt%28149%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0.40<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2813%2Bsqrt%28149%29%29%2F2 ALIGN=MIDDLE  ALT=\"%2813%2Bsqrt%28149%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 12.60<BR>\n" );
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document.write( "There are two solutions.  Because Mike's rate of work is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28x-1%29 ALIGN=MIDDLE  ALT=\"1%2F%28x-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the job per hour, the first solution, x = 0.40, would make Mike's rate of work <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28-0.60%29 ALIGN=MIDDLE  ALT=\"1%2F%28-0.60%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Since this is a negative rate of work, this is impossible.<BR>\n" );
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document.write( "Therefore, we are left with x = 12.60<BR>\n" );
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document.write( "We are looking how long it would have taken Homer to fix the deck working alone.  Homer's rate of work is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fx ALIGN=MIDDLE  ALT=\"1%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the job per hour.  Plugging in x = 12.60, this means Homer's rate of work is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F12.60 ALIGN=MIDDLE  ALT=\"1%2F12.60\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the job per hour.  <b>This means it would have taken Homer 12.60 hours to fix the deck working alone.</b> </SPAN>\n" );
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