document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=838449>Question 838449</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A race has two parts, an 18km run and a 30km canoe race. The canoeists travelled 8km/h faster than the runner. The winning time was exactly 3h. How fast did the runner travel?\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #505382 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=505382\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A race has two parts, an 18km run and a 30km canoe race.<BR>\n" );
document.write( " The canoeists travelled 8km/h faster than the runner.<BR>\n" );
document.write( " The winning time was exactly 3h.<BR>\n" );
document.write( " How fast did the runner travel?<BR>\n" );
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document.write( "let r = runner's speed<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(r+8) = canoe speed<BR>\n" );
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document.write( "Write a time equation; time = dist/speed<BR>\n" );
document.write( "run time + canoe time = 3 hrs<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18%2Fr ALIGN=MIDDLE  ALT=\"18%2Fr\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30%2F%28%28r%2B8%29%29 ALIGN=MIDDLE  ALT=\"30%2F%28%28r%2B8%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 3<BR>\n" );
document.write( "mult by r(r+8), cancel the denominators, you have:<BR>\n" );
document.write( "18(r+8) + 30r = 3r(r+8)<BR>\n" );
document.write( "18r + 144 + 30r = 3r^2 + 24r<BR>\n" );
document.write( "48r + 144 = 3r^2 + 24r<BR>\n" );
document.write( "Combine as a quadratic equation on the right<BR>\n" );
document.write( "0 = 3r^2 + 24r - 48r - 144<BR>\n" );
document.write( "0 = 3r^2 - 24r - 144<BR>\n" );
document.write( "simplify divide by 3<BR>\n" );
document.write( "r^2 - 8r - 48 = 0<BR>\n" );
document.write( "Factors to<BR>\n" );
document.write( "(r+4)(r-12) = 0<BR>\n" );
document.write( "The positive solution<BR>\n" );
document.write( "r = 12 km/h is the runners speed<BR>\n" );
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document.write( "Check this<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18%2F12 ALIGN=MIDDLE  ALT=\"18%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30%2F20 ALIGN=MIDDLE  ALT=\"30%2F20\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <BR>\n" );
document.write( "1.5 + 1.5 = 3<BR>\n" );
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