document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=640870>Question 640870</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Maria lights two candles of equal length at the same time. One candle takes 6 hours to burn out and the other takes 9 hours. How much time will pass until the slower burning candle is exactly twice as long as the faster burning one? Explain your answer. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #403474 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=403474\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Since the candles can be any length, I will say<BR>\n" );
document.write( "they are both <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+18+ ALIGN=MIDDLE  ALT=\"+18+\"   DISABLED_style= \"max-width:90%; height:auto;\" > units long, and the units<BR>\n" );
document.write( "can be anything I choose.<BR>\n" );
document.write( "The fast burning candle burns at a rate of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+18%2F6+=+3+ ALIGN=MIDDLE  ALT=\"+18%2F6+=+3+\"   DISABLED_style= \"max-width:90%; height:auto;\" > units/hr<BR>\n" );
document.write( "The slow burning candle burns at a rate of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+18%2F9+=+2+ ALIGN=MIDDLE  ALT=\"+18%2F9+=+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > units/hr<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+ ALIGN=MIDDLE  ALT=\"+x+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the units that the fast burning candle<BR>\n" );
document.write( "burns off in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+ ALIGN=MIDDLE  ALT=\"+t+\"   DISABLED_style= \"max-width:90%; height:auto;\" > hrs<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+18+-+x+ ALIGN=MIDDLE  ALT=\"+18+-+x+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the length that is left<BR>\n" );
document.write( "It is given that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%2A%28+18+-+x+%29+ ALIGN=MIDDLE  ALT=\"+2%2A%28+18+-+x+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the length left of the slow burning candle<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+18+-+2%2A%28+18+-+x+%29+ ALIGN=MIDDLE  ALT=\"+18+-+2%2A%28+18+-+x+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the length of the slow burning candle<BR>\n" );
document.write( "that has burned away<BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "Equation for fast-burning candle:<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+3t+ ALIGN=MIDDLE  ALT=\"+x+=+3t+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Equation for slow-burning candle:<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+18+-+2%2A%28+18+-+x+%29+=+2t+ ALIGN=MIDDLE  ALT=\"+18+-+2%2A%28+18+-+x+%29+=+2t+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "------------------------<BR>\n" );
document.write( "Substitute (1) into (2)<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+18+-+2%2A%28+18+-+3t+%29+=+2t+ ALIGN=MIDDLE  ALT=\"+18+-+2%2A%28+18+-+3t+%29+=+2t+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+18+-+36+%2B+6t+=+2t+ ALIGN=MIDDLE  ALT=\"+18+-+36+%2B+6t+=+2t+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-18+=+-4t+ ALIGN=MIDDLE  ALT=\"+-18+=+-4t+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+9%2F2+ ALIGN=MIDDLE  ALT=\"+t+=+9%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "In 4 and one half hours the slower burning<BR>\n" );
document.write( "candle is twice as long as the faster burning candle<BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "check:<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+3%2A%289%2F2%29+ ALIGN=MIDDLE  ALT=\"+x+=+3%2A%289%2F2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+27%2F2+ ALIGN=MIDDLE  ALT=\"+x+=+27%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+18+-+2%2A%28+18+-+27%2F2+%29+=+2t+ ALIGN=MIDDLE  ALT=\"+18+-+2%2A%28+18+-+27%2F2+%29+=+2t+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+18+-+2%2A%28+36%2F2+-+27%2F2+%29+=+2t+ ALIGN=MIDDLE  ALT=\"+18+-+2%2A%28+36%2F2+-+27%2F2+%29+=+2t+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+18+-+36+%2B+27+=+2t+ ALIGN=MIDDLE  ALT=\"+18+-+36+%2B+27+=+2t+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+9+=+2t+ ALIGN=MIDDLE  ALT=\"+9+=+2t+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+9%2F2+ ALIGN=MIDDLE  ALT=\"+t+=+9%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );