document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=145749>Question 145749</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Maria lights two candles of equal length at the same time.  One candle takes six hours to burn out and the other takes nine.  How much time will pass until the slower-burning candle is exactly twice as long as the faster-burning one? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #106375 by </B><A HREF=/tutors/aboutme.mpl?userid=ptaylor><B>ptaylor(2198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ptaylor><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=ptaylor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=106375\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let L=length of each candle<BR>\n" );
document.write( "And Let T=time(in hours) that will pass until the slow burning candle is exactly twice as long as the fast burning one\r<BR>\n" );
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document.write( "The fast burning candle burns at the rate of (1/6)L per hour\r<BR>\n" );
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document.write( "And the slow burning candle burns at the rate of (1/9)L per hour\r<BR>\n" );
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document.write( "Now, after T hours the slow burning candle is L-(1/9)L*T long<BR>\n" );
document.write( "And the fast burning candle is L-(1/6)L*T long\r<BR>\n" );
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document.write( "We are told that the slow burning candle is now twice as long as the fast burning candle, so our equation to solve is:<BR>\n" );
document.write( "L-(1/9)L*T=2(L-(1/6)L*T))  simplify\r<BR>\n" );
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document.write( "L-(1/9)L*T=2L-(2/6)L*T  divide each term by L<BR>\n" );
document.write( "1-(1/9)T=2-(2/6)T  subtract 1 from and add (2/6)T to each side<BR>\n" );
document.write( "1-1-(1/9)T+(2/6)T=2-1-(2/6)T+(2/6)T<BR>\n" );
document.write( "-(2/18)T+(6/18)T=1<BR>\n" );
document.write( "(4/18)T=1 multiply each side by 18\r<BR>\n" );
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document.write( "4T=18  divide each side by 4<BR>\n" );
document.write( "T=4.5 hrs ----------------------time needed for slow burning candle to be exactly twice as long as the fast burning candle\r<BR>\n" );
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document.write( "CK\r<BR>\n" );
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document.write( "In 4.5 hours the slow burning candle is (L-(1/9)*4.5L)=(L-0.5L) units long<BR>\n" );
document.write( "In 4.5 hours the fast burning candle is (L-(1/6)*4.5L)+(L-0.75L) units long\r<BR>\n" );
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document.write( "And we are told that:<BR>\n" );
document.write( "(L-0.5L)=2(L-0.75L) or<BR>\n" );
document.write( "0.5L=2(0.25)L<BR>\n" );
document.write( "0.5L=0.5L\r<BR>\n" );
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document.write( "Hope this helps---ptaylor </SPAN>\n" );
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