document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=87074>Question 87074</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I don't know where to begin with this problem!!  Please help.  Thanks you.  \r<BR>\n" );
document.write( "\n" );
document.write( "A candle is lit at 5:30 p.m.  Another candle, 1 cm shorter than the first, is lit at 7 p.m.  The candles are the same length at 9:30 p.m.  The first candle burns out at 11:30 p.m. and the second one at 11:00 p.m.  How tall was the longer candle?   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #63062 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=63062\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Each candle has a rate of burn, and what is being assumed in<BR>\n" );
document.write( "the problem (and of course is debateable) is that the rate of<BR>\n" );
document.write( "burn for each is constant and may be different for each candle.<BR>\n" );
document.write( "The rate of burn is how far it burns down in a given time period.<BR>\n" );
document.write( "First look at when each is lit and when it burns out.<BR>\n" );
document.write( "Call the 1st one candle A and the 2nd one candle B.<BR>\n" );
document.write( "The rate of burn for A is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5BA%5D ALIGN=MIDDLE  ALT=\"r%5BA%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The rate of burn for B is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5BB%5D ALIGN=MIDDLE  ALT=\"r%5BB%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Call <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" > the starting height of A in cm<BR>\n" );
document.write( "The <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h-1 ALIGN=MIDDLE  ALT=\"h-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the starting height of B in cm<BR>\n" );
document.write( "From 5:30 to 11:30 for A is 6 hours<BR>\n" );
document.write( "From 7:00 to 11:00 for B is 4 hours<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5BA%5D+=+h%2F6 ALIGN=MIDDLE  ALT=\"r%5BA%5D+=+h%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5BB%5D+=+%28h-1%29%2F4 ALIGN=MIDDLE  ALT=\"r%5BB%5D+=+%28h-1%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now look at the information relating to the candles being  the same<BR>\n" );
document.write( "height at 9:30. Candle A will burn down the same amount as B plus an<BR>\n" );
document.write( "extra cm.<BR>\n" );
document.write( "So, in words, (A's rate)(A's time) = (B's rate)(B's time) + 1 cm<BR>\n" );
document.write( "A's time is 4 hrs, and B's time is 2.5 hours<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%28h%2F6%29+=+2.5%28%28h-1%29%2F4%29+%2B+1 ALIGN=MIDDLE  ALT=\"4%28h%2F6%29+=+2.5%28%28h-1%29%2F4%29+%2B+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "multiple both sides by LCD which is 12<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+8h+=+3%2A2.5%28h-1%29+%2B+12 ALIGN=MIDDLE  ALT=\"+8h+=+3%2A2.5%28h-1%29+%2B+12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8h+=+%2815%2F2%29%2A%28h-1%29+%2B+12 ALIGN=MIDDLE  ALT=\"8h+=+%2815%2F2%29%2A%28h-1%29+%2B+12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "multiply both sides by 2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16h+=+15h+-+15+%2B+24 ALIGN=MIDDLE  ALT=\"16h+=+15h+-+15+%2B+24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+=+9 ALIGN=MIDDLE  ALT=\"h+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So, the height of the longest candle is 9 cm<BR>\n" );
document.write( "Check this by plugging back into equations<BR>\n" );
document.write( "What are the rates of A and B?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5BA%5D+=+h%2F6 ALIGN=MIDDLE  ALT=\"r%5BA%5D+=+h%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5BA%5D+=+9%2F6 ALIGN=MIDDLE  ALT=\"r%5BA%5D+=+9%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5BA%5D+=+3%2F2 ALIGN=MIDDLE  ALT=\"r%5BA%5D+=+3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5BB%5D+=+%28h-1%29%2F4 ALIGN=MIDDLE  ALT=\"r%5BB%5D+=+%28h-1%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5BB%5D+=+8%2F4 ALIGN=MIDDLE  ALT=\"r%5BB%5D+=+8%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5BB%5D+=+2 ALIGN=MIDDLE  ALT=\"r%5BB%5D+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%28h%2F6%29+=+2.5%28%28h-1%29%2F4%29+%2B+1 ALIGN=MIDDLE  ALT=\"4%28h%2F6%29+=+2.5%28%28h-1%29%2F4%29+%2B+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%283%2F2%29+=+2.5%2A2+%2B+1 ALIGN=MIDDLE  ALT=\"4%283%2F2%29+=+2.5%2A2+%2B+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6+=+5+%2B+1 ALIGN=MIDDLE  ALT=\"6+=+5+%2B+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6+=+6 ALIGN=MIDDLE  ALT=\"6+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "How about the rate*time for each to burn all the way down?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%28h%2F6%29+=+4%28%28h-1%29%2F4%29+%2B+1 ALIGN=MIDDLE  ALT=\"6%28h%2F6%29+=+4%28%28h-1%29%2F4%29+%2B+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "h = 9<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9+=+4%2A2+%2B+1 ALIGN=MIDDLE  ALT=\"9+=+4%2A2+%2B+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9+=+8+%2B+1 ALIGN=MIDDLE  ALT=\"9+=+8+%2B+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9+=+9 ALIGN=MIDDLE  ALT=\"9+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );