document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=468204>Question 468204</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Twin brothers, Billy and Bobby, can mow their grandparent's lawn together in 69 minutes. Billy could mow the lawn by himself in 15 minutes less time that it would take 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 #321262 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=321262\">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 69 minutes. Billy could mow the lawn by himself in 15 minutes less time than it would take Bobby. How long would it take Bobby to mow the lawn by himself?<BR>\n" );
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document.write( "Together time = 69 min/job ; rate = 1/69 job/min<BR>\n" );
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document.write( "Billy time = x-15 min/job ; rate = 1/(x-15) job/min<BR>\n" );
document.write( "------<BR>\n" );
document.write( "Bobby time = x min/job ; rate = 1/x job/min<BR>\n" );
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document.write( "Equation:<BR>\n" );
document.write( "rate + rate = together rate<BR>\n" );
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document.write( "1/x + 1/(x-15) = 1/69<BR>\n" );
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document.write( "69(x-15) + 69x = x(x-15)<BR>\n" );
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document.write( "138x-69*15 = x^2-15x<BR>\n" );
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document.write( "x^2 -15x -138x + 69*15 = 0<BR>\n" );
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document.write( "x^2 - 153x + 69*15 = 0<BR>\n" );
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document.write( "x = [153 +- sqrt(153^2 - 4*69*15)/2<BR>\n" );
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document.write( "x = [153 +- sqrt(19269)]/2<BR>\n" );
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document.write( "Realistic answer:<BR>\n" );
document.write( "x = 145.91 minutes (Bobby's time)<BR>\n" );
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document.write( "x-15 = 130.91 minutes (Billy's time)<BR>\n" );
document.write( "======================================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "=============== </SPAN>\n" );
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