document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=613389>Question 613389</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A high school track coach determines that his fastest long distance runner runs 2 miles per hour faster than his slowest runner. Compared to the faster runner, the slower runner takes a half hour longer to run 12 miles.\r<BR>\n" );
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document.write( "a. Find the average rates of both runners.<BR>\n" );
document.write( "b. Find the time for both runners to run 12 miles. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #386041 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=386041\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A high school track coach determines that his fastest long distance runner runs 2 miles per hour faster than his slowest runner.<BR>\n" );
document.write( " Compared to the faster runner, the slower runner takes a half hour longer to run 12 miles.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "a. Find the average rates of both runners.<BR>\n" );
document.write( "Let s = speed of the slower runner<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(s+2) = speed of the faster runner<BR>\n" );
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document.write( "Write a time equation; time = dist/speed<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2Fs ALIGN=MIDDLE  ALT=\"12%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2F%28%28s%2B2%29%29 ALIGN=MIDDLE  ALT=\"12%2F%28%28s%2B2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = .5 hr<BR>\n" );
document.write( "Multiply s(s+2), results:<BR>\n" );
document.write( "12(s+2) - 12s = .5s(s+2)<BR>\n" );
document.write( "12s + 24 - 12s = .5s^2 + s<BR>\n" );
document.write( "0 = .5s^2 + s - 24<BR>\n" );
document.write( "multiply by 2, to get rid of the decimal<BR>\n" );
document.write( "s^2 + 2s - 48 = 0<BR>\n" );
document.write( "Factors to<BR>\n" );
document.write( "(s+8)(s-6) = 0<BR>\n" );
document.write( "The positive solution<BR>\n" );
document.write( "s = 6 mph the slow runner<BR>\n" );
document.write( "then<BR>\n" );
document.write( "6 + 2 = 8 mph is the faster runner<BR>\n" );
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document.write( "b. Find the time for both runners to run 12 miles.<BR>\n" );
document.write( "12/8 = 1.5 hrs the faster runner<BR>\n" );
document.write( "12/6 = 2 hrs the slower\r<BR>\n" );
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document.write( " </SPAN>\n" );
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