document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=468235>Question 468235</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Twin brothers Billy and bobby, can mow their grandparents lawn together in 108 minutes. Billy could now mow the lawn by himself in 35 minutes less time that it would bobby. How long would it take bobby to mow the lawn by himself? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #321382 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=321382\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Billy and bobby, can mow their grandparents lawn together in 108 minutes.<BR>\n" );
document.write( " Billy could now mow the lawn by himself in 35 minutes less time that it would bobby.<BR>\n" );
document.write( " How long would it take bobby to mow the lawn by himself?<BR>\n" );
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document.write( "Let t = time for Bob to mow by himself<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(t-35) = time for Bill to do it by himself<BR>\n" );
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document.write( "Let the completed job = 1 (a mowed lawn)<BR>\n" );
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document.write( "A typical shared work equation<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=108%2Ft ALIGN=MIDDLE  ALT=\"108%2Ft\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=108%2F%28%28t-35%29%29 ALIGN=MIDDLE  ALT=\"108%2F%28%28t-35%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( "Multiply by t(t-35), results:<BR>\n" );
document.write( "108(t-35) + 108t = t(t-35)<BR>\n" );
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document.write( "108t - 3780 + 108t = t^2 - 35t<BR>\n" );
document.write( "216t - 3780 = t^2 - 35t<BR>\n" );
document.write( "Arrange as a quadratic equation<BR>\n" );
document.write( "0 = t^2 - 35t - 216t + 3780<BR>\n" );
document.write( "t^2 - 251t + 3780 = 0<BR>\n" );
document.write( "Use the quadratic formula to find t<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "In this equation x=t, a=1, b= -251, c= 3780<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-%28-251%29+%2B-+sqrt%28-251%5E2-4%2A1%2A3780+%29%29%2F%282%2A1%29+ ALIGN=MIDDLE  ALT=\"t+=+%28-%28-251%29+%2B-+sqrt%28-251%5E2-4%2A1%2A3780+%29%29%2F%282%2A1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28251+%2B-+sqrt%2863001-15120+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"t+=+%28251+%2B-+sqrt%2863001-15120+%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28251+%2B-+sqrt%2847881+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"t+=+%28251+%2B-+sqrt%2847881+%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Two solutions<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28251+%2B+218.8%29%2F2+ ALIGN=MIDDLE  ALT=\"t+=+%28251+%2B+218.8%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "t = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=469.8%2F2 ALIGN=MIDDLE  ALT=\"469.8%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "t = 234.9 <BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28251+-+218.8%29%2F2+ ALIGN=MIDDLE  ALT=\"t+=+%28251+-+218.8%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "t = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=32.2%2F2 ALIGN=MIDDLE  ALT=\"32.2%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "t = 16.1<BR>\n" );
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document.write( "Only the first solution will make sense, t ~ 235 min, Bob by himself<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Check this (200 min for Bill)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=108%2F235 ALIGN=MIDDLE  ALT=\"108%2F235\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=108%2F200 ALIGN=MIDDLE  ALT=\"108%2F200\"   DISABLED_style= \"max-width:90%; height:auto;\" > =<BR>\n" );
document.write( ".46 + .54 = 1<BR>\n" );
document.write( " <BR>\n" );
document.write( ":\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );