document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1146675>Question 1146675</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two different candles are lit. They burn at different rates and one is 3 cm longer than the other. The longer one was lit at 5:30 pm and the shorter one at 7 pm. At 9:30 pm they were both the same length. The longer one burned out at 11:30 pm and the shorter one burned out at 11 pm. How long was each candle originally? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #767963 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=767963\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Two different candles are lit.<BR>\n" );
document.write( " They burn at different rates and one is 3 cm longer than the other.<BR>\n" );
document.write( " The longer one was lit at 5:30 pm and the shorter one at 7 pm.<BR>\n" );
document.write( " At 9:30 pm they were both the same length.<BR>\n" );
document.write( " The longer one burned out at 11:30 pm and the shorter one burned out at 11 pm.<BR>\n" );
document.write( " How long was each candle originally?<BR>\n" );
document.write( ":<BR>\n" );
document.write( "let a = the length of the longer candle<BR>\n" );
document.write( "let b = the length of the shorter<BR>\n" );
document.write( " :<BR>\n" );
document.write( "the longer candle burned from 5:30 to 11:30 or 6 hrs, therefore<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2F6 ALIGN=MIDDLE  ALT=\"a%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > cm/hr is the rate of burn of the longer<BR>\n" );
document.write( "and<BR>\n" );
document.write( "the shorter candle burned from 7:00 to 11:00 or 4 hrs, therefore<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2F4 ALIGN=MIDDLE  ALT=\"b%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > cm/hr is the rate of burn for the shorter candle<BR>\n" );
document.write( ":<BR>\n" );
document.write( "at 9:30 the longer candle has burned for 4 hrs and the shorter for 2.5 hrs<BR>\n" );
document.write( "a - 4*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2F6 ALIGN=MIDDLE  ALT=\"a%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > = b - 2.5*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2F4 ALIGN=MIDDLE  ALT=\"b%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4a%2F6 ALIGN=MIDDLE  ALT=\"4a%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > = b - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2.5b%2F4 ALIGN=MIDDLE  ALT=\"2.5b%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "multiply both sides by 12, get rid of the denominator<BR>\n" );
document.write( "12a - 8a = 12b - 7.5b<BR>\n" );
document.write( "4a = 4.5b<BR>\n" );
document.write( "a is 3 cm longer than b, therefore<BR>\n" );
document.write( "replace b with (a-3)<BR>\n" );
document.write( "4a = 4.5(a-3)<BR>\n" );
document.write( "4a = 4.5a - 13.5<BR>\n" );
document.write( "4a - 4.5a = -13.5<BR>\n" );
document.write( "-.5a = -13.5<BR>\n" );
document.write( "a = -13.5/-.5<BR>\n" );
document.write( "a = 27 cm is the longer candle<BR>\n" );
document.write( "and obviously<BR>\n" );
document.write( "24 cm is the shorter\r<BR>\n" );
document.write( "\n" );
document.write( ":<BR>\n" );
document.write( "see of this works out<BR>\n" );
document.write( "27/6 = 4.5 cm/hr burn rate of the longer<BR>\n" );
document.write( "24/4 = 6 cm/hr is the rate of the shorter<BR>\n" );
document.write( ":<BR>\n" );
document.write( "27 - 4(4.5) = <BR>\n" );
document.write( "27 - 18 = 9 cm remain<BR>\n" );
document.write( "and<BR>\n" );
document.write( "24 - 2.5(6) = <BR>\n" );
document.write( "24 - 15 = 9 cm remain </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );