document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=563341>Question 563341</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Twin brothers, Billy and Bobby, can mow their grandparent's lawn together in 102 minutes. Billy could mow the lawn by himself in 20 minutes less time that it would take bobby. How long would it take bobby to mow the law 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 #364872 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=364872\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Twin brothers, Billy and Bobby, can mow their grandparent's lawn together in 102 minutes.<BR>\n" );
document.write( " Billy could mow the lawn by himself in 20 minutes less time that it would take bobby.<BR>\n" );
document.write( " How long would it take bobby to mow the law by himself?<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let b = Bobby's time by himself<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(b-20) = Billy's time by himself<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let the completed job = 1 (a mowed lawn)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=102%2F%28%28b-20%29%29 ALIGN=MIDDLE  ALT=\"102%2F%28%28b-20%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=102%2Fb ALIGN=MIDDLE  ALT=\"102%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( "Multiply by b(b-20)<BR>\n" );
document.write( "b(b-20)*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=102%2F%28%28b-20%29%29 ALIGN=MIDDLE  ALT=\"102%2F%28%28b-20%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + b(b-20)*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=102%2Fb ALIGN=MIDDLE  ALT=\"102%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" > = b(b-20)<BR>\n" );
document.write( "Cancel the denominators and you have:<BR>\n" );
document.write( "102b + 102(b-20) = b^2 - 20b<BR>\n" );
document.write( "102b + 102b - 2040 = b^2 - 20b<BR>\n" );
document.write( "204b - 2040 = b^2 - 20b<BR>\n" );
document.write( "combine as quadratic equation on the right<BR>\n" );
document.write( "0 = b^2 - 20b - 204b + 2040<BR>\n" );
document.write( "b^2 - 224b + 2040 = 0<BR>\n" );
document.write( "Use the quadratic formula to find b<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 problem;  a=1; b=-224; c=2040<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+%28-%28224%29+%2B-+sqrt%28-224%5E2-4%2A1%2A2040+%29%29%2F%282%2A1%29+ ALIGN=MIDDLE  ALT=\"b+=+%28-%28224%29+%2B-+sqrt%28-224%5E2-4%2A1%2A2040+%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=b+=+%28224+%2B-+sqrt%2850176-8160+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"b+=+%28224+%2B-+sqrt%2850176-8160+%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=b+=+%28224+%2B-+sqrt%2842016+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"b+=+%28224+%2B-+sqrt%2842016+%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Two solutions, but only this one will make sense<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+%28224+%2B+205%29%2F2+ ALIGN=MIDDLE  ALT=\"b+=+%28224+%2B+205%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "b = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=429%2F2 ALIGN=MIDDLE  ALT=\"429%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "b = 214.5 minutes for Bobby to do the job alone<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Check this (Billy's time 214.5 - 20 = 194.5)<BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=102%2F194.5 ALIGN=MIDDLE  ALT=\"102%2F194.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=102%2F214.5 ALIGN=MIDDLE  ALT=\"102%2F214.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <BR>\n" );
document.write( ".524 + .476 = 1; confirms our solution of b - 214.5 min </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );