document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=557423>Question 557423</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The first two sections of a bicycle race are x and y meters long. Annie cycles the first part of the race at 6m/s and the second part at 12m/s. Barry cycles the same sections at 10m/s and 6m/s. It takes Annie half a minute to cycle these two sections, whereas it takes Barry 46 seconds to cover the same distance. \r<BR>\n" );
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document.write( "How long are these two sections of the race?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #362860 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=362860\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The first two sections of a bicycle race are x and y meters long.<BR>\n" );
document.write( " Annie cycles the first part of the race at 6m/s and the second part at 12m/s<BR>\n" );
document.write( " Barry cycles the same sections at 10m/s and 6m/s. It takes Annie half a minute to cycle these two sections, whereas it takes Barry 46 seconds to cover the same distance.<BR>\n" );
document.write( "How long are these two sections of the race? <BR>\n" );
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document.write( "Write a time equation for each; time = dist/speed. simplify each equation<BR>\n" );
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document.write( "First cyclist: <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F6 ALIGN=MIDDLE  ALT=\"x%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2F12 ALIGN=MIDDLE  ALT=\"y%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 30<BR>\n" );
document.write( "Multiply by 12, to clear the denominators, results<BR>\n" );
document.write( "2x + y = 360<BR>\n" );
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document.write( "2nd cyclist: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F10 ALIGN=MIDDLE  ALT=\"x%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2F6 ALIGN=MIDDLE  ALT=\"y%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 46<BR>\n" );
document.write( "multiply by 30<BR>\n" );
document.write( "3x + 5y = 1380<BR>\n" );
document.write( "Multiply the 1st equation by 5, subtract the above equation<BR>\n" );
document.write( "10x + 5y = 1800<BR>\n" );
document.write( "3x + 5y = 1380<BR>\n" );
document.write( "----------------subtraction eliminates y, find x<BR>\n" );
document.write( "7x = 420<BR>\n" );
document.write( "x = 420/7<BR>\n" );
document.write( "x = 60 meters is the 1st part<BR>\n" );
document.write( "and<BR>\n" );
document.write( "y = -2x + 360<BR>\n" );
document.write( "y = -2(60) + 360<BR>\n" );
document.write( "y = 240 meters is the 2nd part<BR>\n" );
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document.write( "Check this; find the time of the 1st cyclist<BR>\n" );
document.write( "60/6 + 240/12<BR>\n" );
document.write( "10 + 20 = 30 sec<BR>\n" );
document.write( "and the 2nd cyclist time<BR>\n" );
document.write( "60/10 + 240/6 = <BR>\n" );
document.write( "6 + 40 = 46 sec<BR>\n" );
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