document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1068309>Question 1068309</A>: <I><SPAN STYLE=\"word-break: break-all;\"> There are 2 candles, one shorter than the other, which are lit at the same time.<BR>\n" );
document.write( "After a while the longer one is 12cm in height while the other one is 5cm shorter than it's beginning lenght.<BR>\n" );
document.write( "You know that the shorter candle burns half as fast as the longer one.<BR>\n" );
document.write( "What's their lenght on the exact moment when they're both equal in lenght? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #683554 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=683554\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Either a piece of information was lost somewhere along the way,<BR>\n" );
document.write( "or this is a problem where you are supposed to say that there is not enough information.<BR>\n" );
document.write( "There is no unique solution.<BR>\n" );
document.write( "Maybe you have to write 2 equations with 3 variables and say that the system is \"undetermined\".<BR>\n" );
document.write( " <BR>\n" );
document.write( "We know that after a while,<BR>\n" );
document.write( "the originally shorter candle is 5cm shorter than its original height.<BR>\n" );
document.write( "At that point, the originally longer candle, which burns twice as fast,<BR>\n" );
document.write( "must be 10cm shorter than it originally was.<BR>\n" );
document.write( "That means that the longer candle v was originally 22cm long.<BR>\n" );
document.write( "It also means, that at 10cm per \"while\",<BR>\n" );
document.write( "it will be completely burnt after 2.2 \"whiles.\"<BR>\n" );
document.write( "The shorter candle musty have originally been less than 22cm long.<BR>\n" );
document.write( "We do not know the original height,<BR>\n" );
document.write( "but the original height makes a difference.<BR>\n" );
document.write( "If the original height is 11cm,<BR>\n" );
document.write( "at 5cm per while, it would completely burn in 2.2 \"whiles,\"<BR>\n" );
document.write( "just v like the longer candle,<BR>\n" );
document.write( "so the answer would be 0cm,<BR>\n" );
document.write( "meaning they would be equally long when they are both burnt up.<BR>\n" );
document.write( "If the shorter candle starts with a length of 16 cm,<BR>\n" );
document.write( "The 22cm-17cm=5cm difference will decrease (at 5cm per \"while\")<BR>\n" );
document.write( "to 0cm in exactly 1 while,<BR>\n" );
document.write( "and at that point both candles will be 12cm long.<BR>\n" );
document.write( "If you pick another initial length for the shorter candle,<BR>\n" );
document.write( "you get another result.<BR>\n" );
document.write( "Maybe the shorter candle started with a 14cm length,<BR>\n" );
document.write( "and after 1.6 while both candles are 6cm long.<BR>\n" );
document.write( "Maybe the short candle was initially 21cm long,<BR>\n" );
document.write( "and 0.2 while later both candles were 20 cm long. </SPAN>\n" );
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