document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=477023>Question 477023</A>: <I><SPAN STYLE=\"word-break: break-all;\"> two candles of the same height are lit at the same time. each candle burns at a constant rate and the first candle takes 5 hours while the second candle takes 4 hours to burn completely. find the time, in hours, taken for the height of the first candle to be four time that of the second candle </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #327061 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=327061\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%5B0%5D+ ALIGN=MIDDLE  ALT=\"+h%5B0%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the height that both candles start at<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%5B1%5D+ ALIGN=MIDDLE  ALT=\"+h%5B1%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the current height of the 1st candle<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%5B2%5D+ ALIGN=MIDDLE  ALT=\"+h%5B2%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the current height of the 2nd candle<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+ ALIGN=MIDDLE  ALT=\"+t+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the current time expired in hours<BR>\n" );
document.write( "given:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%5B0%5D+%2F+5+ ALIGN=MIDDLE  ALT=\"+h%5B0%5D+%2F+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the rate of burning of the 1st candle<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%5B0%5D+%2F+4+ ALIGN=MIDDLE  ALT=\"+h%5B0%5D+%2F+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the rate of burning of the 2nd candle<BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "For the 1st candle:<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%5B1%5D+=+h%5B0%5D+-+%28+h%5B0%5D%2F5+%29%2At+ ALIGN=MIDDLE  ALT=\"+h%5B1%5D+=+h%5B0%5D+-+%28+h%5B0%5D%2F5+%29%2At+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "For the 2nd candle:<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%5B2%5D+=+h%5B0%5D+-+%28+h%5B0%5D%2F4+%29%2At+ ALIGN=MIDDLE  ALT=\"+h%5B2%5D+=+h%5B0%5D+-+%28+h%5B0%5D%2F4+%29%2At+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "given:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%5B1%5D+=+4h%5B2%5D+ ALIGN=MIDDLE  ALT=\"+h%5B1%5D+=+4h%5B2%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4h%5B2%5D+=+h%5B0%5D%2A%281+-+t%2F5%29+ ALIGN=MIDDLE  ALT=\"+4h%5B2%5D+=+h%5B0%5D%2A%281+-+t%2F5%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=+h%5B2%5D+=+%28+h%5B0%5D%2A%281+-+t%2F5%29%29%2F4+ ALIGN=MIDDLE  ALT=\"+h%5B2%5D+=+%28+h%5B0%5D%2A%281+-+t%2F5%29%29%2F4+\"   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=+h%5B2%5D+=+h%5B0%5D%2A%281+-+t%2F4%29+ ALIGN=MIDDLE  ALT=\"+h%5B2%5D+=+h%5B0%5D%2A%281+-+t%2F4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "------------------------<BR>\n" );
document.write( "I can set the right sides equal to each other<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+h%5B0%5D%2A%281+-+t%2F5%29%29%2F4+=+h%5B0%5D%2A%281+-+t%2F4%29+ ALIGN=MIDDLE  ALT=\"+%28+h%5B0%5D%2A%281+-+t%2F5%29%29%2F4+=+h%5B0%5D%2A%281+-+t%2F4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%5B0%5D+ ALIGN=MIDDLE  ALT=\"+h%5B0%5D+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++%281+-+t%2F5%29%2F4+=+1+-+t%2F4+ ALIGN=MIDDLE  ALT=\"++%281+-+t%2F5%29%2F4+=+1+-+t%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1+-+t%2F5+=+4+-+t+ ALIGN=MIDDLE  ALT=\"+1+-+t%2F5+=+4+-+t+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+5+-+t+=+20+-+5t+ ALIGN=MIDDLE  ALT=\"+5+-+t+=+20+-+5t+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4t+=+20+-+5+ ALIGN=MIDDLE  ALT=\"+4t+=+20+-+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4t+=+15+ ALIGN=MIDDLE  ALT=\"+4t+=+15+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+3.75+ ALIGN=MIDDLE  ALT=\"+t+=+3.75+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "It will take 3 hrs and 45 min for the <BR>\n" );
document.write( "1st candle to be 4 times as high as the 2nd candle<BR>\n" );
document.write( "check answer:<BR>\n" );
document.write( "Suppose the heights of both start at 1 m<BR>\n" );
document.write( "For the 1st candle:<BR>\n" );
document.write( "For the 1st candle:<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%5B1%5D+=+1+-+%28+1%2F5+%29%2A3.75+ ALIGN=MIDDLE  ALT=\"+h%5B1%5D+=+1+-+%28+1%2F5+%29%2A3.75+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%5B1%5D+=+1+-+.2%2A3.75+ ALIGN=MIDDLE  ALT=\"+h%5B1%5D+=+1+-+.2%2A3.75+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%5B1%5D+=+1+-+.75+ ALIGN=MIDDLE  ALT=\"+h%5B1%5D+=+1+-+.75+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%5B1%5D+=+.25+ ALIGN=MIDDLE  ALT=\"+h%5B1%5D+=+.25+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "For the 2nd candle:<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%5B2%5D+=+1+-+%28+1%2F4+%29%2A3.75+ ALIGN=MIDDLE  ALT=\"+h%5B2%5D+=+1+-+%28+1%2F4+%29%2A3.75+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%5B2%5D+=+1+-+.25%2A3.75+ ALIGN=MIDDLE  ALT=\"+h%5B2%5D+=+1+-+.25%2A3.75+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%5B2%5D+=+1+-+.9375+ ALIGN=MIDDLE  ALT=\"+h%5B2%5D+=+1+-+.9375+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%5B2%5D+=+.0625+ ALIGN=MIDDLE  ALT=\"+h%5B2%5D+=+.0625+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%5B1%5D+%2F+h%5B2%5D+=+.25%2F.0625+ ALIGN=MIDDLE  ALT=\"+h%5B1%5D+%2F+h%5B2%5D+=+.25%2F.0625+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+h%5B1%5D+%2F+h%5B2%5D+=+4+ ALIGN=MIDDLE  ALT=\"+h%5B1%5D+%2F+h%5B2%5D+=+4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );