document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1201875>Question 1201875</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two cars are travelling in opposite directions at different rates.two hours later ,the cars are 110 mi apart.express the distance travelled by the slower car </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #836425 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=836425\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "x = slower speed<BR>\n" );
document.write( "x+k = faster speed<BR>\n" );
document.write( "where k is some positive real number, k > 0\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B1%5D ALIGN=MIDDLE  ALT=\"d%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = distance traveled by the slower car<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B2%5D ALIGN=MIDDLE  ALT=\"d%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = distance traveled by the faster car\r<BR>\n" );
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document.write( "Slower car:<BR>\n" );
document.write( "distance = rate*time<BR>\n" );
document.write( "d = r*t<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B1%5D ALIGN=MIDDLE  ALT=\"d%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = x*2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B1%5D ALIGN=MIDDLE  ALT=\"d%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 2x\r<BR>\n" );
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document.write( "Faster car:<BR>\n" );
document.write( "d = r*t<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B2%5D ALIGN=MIDDLE  ALT=\"d%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = (x+k)*2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B2%5D ALIGN=MIDDLE  ALT=\"d%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 2x+2k<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B2%5D ALIGN=MIDDLE  ALT=\"d%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B1%5D ALIGN=MIDDLE  ALT=\"d%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >+2k\r<BR>\n" );
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document.write( "Their individual travel distances add together to get the total distance between them, because the cars travel in opposite directions. <BR>\n" );
document.write( "Draw out a number line to see why this is the case.<BR>\n" );
document.write( "I'll assume the cars start off at the same location.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B1%5D ALIGN=MIDDLE  ALT=\"d%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >+<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B2%5D ALIGN=MIDDLE  ALT=\"d%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 110<BR>\n" );
document.write( "2x+2x+2k = 110<BR>\n" );
document.write( "4x+2k = 110<BR>\n" );
document.write( "2(2x+k) = 110<BR>\n" );
document.write( "2x+k = 110/2<BR>\n" );
document.write( "2x+k = 55<BR>\n" );
document.write( "2x = 55-k<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B1%5D ALIGN=MIDDLE  ALT=\"d%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 55-k<BR>\n" );
document.write( "If we knew the value of k, then we can find the distance the slower car traveled.\r<BR>\n" );
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document.write( "To avoid <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B1%5D ALIGN=MIDDLE  ALT=\"d%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > being zero or negative, we must have 55-k > 0 which leads to k < 55\r<BR>\n" );
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document.write( "Earlier it was mentioned that k > 0<BR>\n" );
document.write( "So 0 < k < 55<BR>\n" );
document.write( "</font> </SPAN>\n" );
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