document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=96972>Question 96972</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A bike race consists of two segments whose total length is 90 km.  The first segment is covered at 10 kph and takes 2 hours longer to complete than the second segment, which is covered at 25 kph.  How long is each segment?\r<BR>\n" );
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document.write( "I have tried setting it up as t/25 = (t+2)/10 but for some reason I can't figure out the algebra.\r<BR>\n" );
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document.write( "Thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #70600 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=70600\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> From your equation, it appears that you assumed that the two segments were the same distance, but there is nothing in the problem to support this assumption.<BR>\n" );
document.write( "So, back to basics:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B1%5D+=+r%5B1%5Dt%5B1%5D ALIGN=MIDDLE  ALT=\"d%5B1%5D+=+r%5B1%5Dt%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > and...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B2%5D+=+r%5B2%5Dt%5B2%5D ALIGN=MIDDLE  ALT=\"d%5B2%5D+=+r%5B2%5Dt%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We know that:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5B1%5D+=+10 ALIGN=MIDDLE  ALT=\"r%5B1%5D+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" > and...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5B2%5D+=+25 ALIGN=MIDDLE  ALT=\"r%5B2%5D+=+25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5B1%5D+=+t%5B2%5D+%2B+2 ALIGN=MIDDLE  ALT=\"t%5B1%5D+=+t%5B2%5D+%2B+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and we also know that:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B1%5D%2Bd%5B2%5D+=+90 ALIGN=MIDDLE  ALT=\"d%5B1%5D%2Bd%5B2%5D+=+90\"   DISABLED_style= \"max-width:90%; height:auto;\" > So we can write:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B1%5D+=+10t%5B1%5D ALIGN=MIDDLE  ALT=\"d%5B1%5D+=+10t%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B2%5D+=+25t%5B2%5D ALIGN=MIDDLE  ALT=\"d%5B2%5D+=+25t%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > aagh...to many variables! Let's replace <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5B1%5D ALIGN=MIDDLE  ALT=\"t%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5B2%5D%2B2 ALIGN=MIDDLE  ALT=\"t%5B2%5D%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and replace <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;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=90-d%5B1%5D ALIGN=MIDDLE  ALT=\"90-d%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so now we have:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B1%5D+=+10%28t%5B2%5D%2B2%29 ALIGN=MIDDLE  ALT=\"d%5B1%5D+=+10%28t%5B2%5D%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=90-d%5B1%5D+=+25t%5B2%5D ALIGN=MIDDLE  ALT=\"90-d%5B1%5D+=+25t%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > Solve this for <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;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B1%5D+=+90-25t%5B2%5D ALIGN=MIDDLE  ALT=\"d%5B1%5D+=+90-25t%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >...but, of course, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B1%5D+=+d%5B1%5D ALIGN=MIDDLE  ALT=\"d%5B1%5D+=+d%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%28t%5B2%5D%2B2%29+=+90-25t%5B2%5D ALIGN=MIDDLE  ALT=\"10%28t%5B2%5D%2B2%29+=+90-25t%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > Good, now we have one variable <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5B2%5D ALIGN=MIDDLE  ALT=\"t%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so let's solve for it.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10t%5B2%5D%2B20+=+90-25t%5B2%5D ALIGN=MIDDLE  ALT=\"10t%5B2%5D%2B20+=+90-25t%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=35t%5B2%5D%2B20+=+90 ALIGN=MIDDLE  ALT=\"35t%5B2%5D%2B20+=+90\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=35t%5B2%5D+=+70 ALIGN=MIDDLE  ALT=\"35t%5B2%5D+=+70\"   DISABLED_style= \"max-width:90%; height:auto;\" > and...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5B2%5D+=+2 ALIGN=MIDDLE  ALT=\"t%5B2%5D+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >hrs. Now we can find <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;\" > and <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;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B1%5D+=+10%28t%5B2%5D%2B2%29 ALIGN=MIDDLE  ALT=\"d%5B1%5D+=+10%28t%5B2%5D%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B1%5D+=+10%282%2B2%29 ALIGN=MIDDLE  ALT=\"d%5B1%5D+=+10%282%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B1%5D+=+40 ALIGN=MIDDLE  ALT=\"d%5B1%5D+=+40\"   DISABLED_style= \"max-width:90%; height:auto;\" >km and...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B2%5D+=+90-d%5B1%5D ALIGN=MIDDLE  ALT=\"d%5B2%5D+=+90-d%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B2%5D+=+90-40 ALIGN=MIDDLE  ALT=\"d%5B2%5D+=+90-40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B2%5D+=+50 ALIGN=MIDDLE  ALT=\"d%5B2%5D+=+50\"   DISABLED_style= \"max-width:90%; height:auto;\" >km\r<BR>\n" );
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document.write( "Check:<BR>\n" );
document.write( "Total distance is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B1%5D%2Bd%5B2%5D+=+40%2B50 ALIGN=MIDDLE  ALT=\"d%5B1%5D%2Bd%5B2%5D+=+40%2B50\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 90km </SPAN>\n" );
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