document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1197454>Question 1197454</A>: <I><SPAN STYLE=\"word-break: break-all;\"> please help my friend's homework hehe thankyou<BR>\n" );
document.write( "Mike and gerry can finish building a doghouse in 4 hours. It would take mike 6 more hours that gerry to finish the job working alone. How long would it take each boy if each works alone? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #830728 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52781)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=830728\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "Mike and gerry can finish building a doghouse in 4 hours. <BR>\n" );
document.write( "It would take mike 6 more hours <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28cross%28that%29%29 ALIGN=MIDDLE  ALT=\"highlight%28cross%28that%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <U>THAN</U> gerry to finish the job working alone. <BR>\n" );
document.write( "How long would it take each boy if each works alone?<BR>\n" );
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document.write( "Let &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >&nbsp; be the number of hours for gerry to cover the roof, &nbsp;working alone.<BR>\n" );
document.write( "If Mike works alone, &nbsp;he can complete this job in &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B6 ALIGN=MIDDLE  ALT=\"x%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" >&nbsp; hours.<BR>\n" );
document.write( "Thus, &nbsp;in one single day Mike covers &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28x%2B6%29 ALIGN=MIDDLE  ALT=\"1%2F%28x%2B6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >&nbsp; part of the roof area, &nbsp;while gerry covers &nbsp;<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;\" >&nbsp; part of the roof area.<BR>\n" );
document.write( "Working together, &nbsp;Mike and gerry make &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F%28x%2B6%29%2B1%2Fx ALIGN=MIDDLE  ALT=\"1%2F%28x%2B6%29%2B1%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" >&nbsp; of the whole work in each single day.<BR>\n" );
document.write( "Since they can cover the entire roof in &nbsp;6&nbsp; hours working together, &nbsp;the equation for the unknown value &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >&nbsp; is as follows:\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F%28x%2B6%29+%2B+4%2Fx+=+1 ALIGN=MIDDLE  ALT=\"4%2F%28x%2B6%29+%2B+4%2Fx+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "To simplify this equation, &nbsp;multiply both sides by &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B6%29%2Ax ALIGN=MIDDLE  ALT=\"%28x%2B6%29%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" >, &nbsp;then transfer all terms <BR>\n" );
document.write( "from the right side to the left with the opposite signs, &nbsp;collect the common terms <BR>\n" );
document.write( "and adjust the signs. &nbsp;In this way you get\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x+%2B+4%28x%2B6%29+=+x%28x%2B6%29 ALIGN=MIDDLE  ALT=\"4x+%2B+4%28x%2B6%29+=+x%28x%2B6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x+%2B+4x+%2B24+=+x%5E2%2B6x ALIGN=MIDDLE  ALT=\"4x+%2B+4x+%2B24+=+x%5E2%2B6x\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B6x-4x-4x-24+=+0 ALIGN=MIDDLE  ALT=\"x%5E2%2B6x-4x-4x-24+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-2x-24+=+0 ALIGN=MIDDLE  ALT=\"x%5E2-2x-24+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,\r<BR>\n" );
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document.write( "You get the quadratic equation. &nbsp;It is factorable\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(x-6)*(x+4) = 0\r<BR>\n" );
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document.write( "The equation has two roots: &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D=+6 ALIGN=MIDDLE  ALT=\"x%5B1%5D=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" >&nbsp; and &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D=+-4 ALIGN=MIDDLE  ALT=\"x%5B2%5D=+-4\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "The second root &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D=+-2 ALIGN=MIDDLE  ALT=\"x%5B2%5D=+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >&nbsp; makes no sense and we decline it. \r<BR>\n" );
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document.write( "So, &nbsp;the potentially correct solution is &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D=+6 ALIGN=MIDDLE  ALT=\"x%5B1%5D=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" >: &nbsp;gerry covers the roof in &nbsp;6&nbsp; hours working alone.<BR>\n" );
document.write( "Hence, Mike can complete the job in 6+6 = 12 hours.\r<BR>\n" );
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document.write( "Let us check it. \r<BR>\n" );
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document.write( "Since &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2F12%2B4%2F6 ALIGN=MIDDLE  ALT=\"4%2F12%2B4%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3+%2B+2%2F3 ALIGN=MIDDLE  ALT=\"1%2F3+%2B+2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, &nbsp;this solution is correct.\r<BR>\n" );
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document.write( "<B>Answer</B>. &nbsp;gerry can finish the job in &nbsp;6&nbsp; hours working alone.  &nbsp;Mike can complete the job in &nbsp;12 &nbsp;hours.\r<BR>\n" );
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document.write( "Solved.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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