document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=970270>Question 970270</A>: <I><SPAN STYLE=\"word-break: break-all;\"> in a biathlon run over a 16 km (each way) course, the first half is the outgoing leg which is running and the returns section is covered by bicycle. Sam takes 1 hour 15 min. on the run leg. What speed must Sam cycle the returns leg to bring about a 50% improvement on his average speed for the entire race ? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #592922 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=592922\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  In a biathlon run over a 16 km (each way) course, the first half is the outgoing leg which is running and the returns section is covered by bicycle.<BR>\n" );
document.write( " Sam takes 1 hour 15 min. on the run leg.<BR>\n" );
document.write( " What speed must Sam cycle the returns leg to bring about a 50% improvement on his average speed for the entire race ?<BR>\n" );
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document.write( "Find the average speed on the run leg, 1 hr 15min = 1.25 hrs<BR>\n" );
document.write( "16/1.25 = 12.8 km/hr<BR>\n" );
document.write( "Find the 50% improvement in speed<BR>\n" );
document.write( "1.5 * 12.8 = 19.2 km/hr<BR>\n" );
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document.write( "let s = speed required on the return trip to average 19.2 km/hr<BR>\n" );
document.write( "Write a time equation; time = dist/speed<BR>\n" );
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document.write( "run time + bike time = total time<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%2F12.8 ALIGN=MIDDLE  ALT=\"16%2F12.8\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%2Fs ALIGN=MIDDLE  ALT=\"16%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=32%2F19.2 ALIGN=MIDDLE  ALT=\"32%2F19.2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Reduce fractions<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F4 ALIGN=MIDDLE  ALT=\"5%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%2Fs ALIGN=MIDDLE  ALT=\"16%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F3 ALIGN=MIDDLE  ALT=\"5%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "multiply by 12s, cancel the denominators and we have<BR>\n" );
document.write( "3s(5) + 12(16) = 4s(5)<BR>\n" );
document.write( "15s + 192 = 20s<BR>\n" );
document.write( "192 = 20s - 15s<BR>\n" );
document.write( "192 = 5s<BR>\n" );
document.write( "s = 192/5<BR>\n" );
document.write( "s = 38.4 km/hr, ride his bike on the return leg to average 19.2 km/hr\r<BR>\n" );
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document.write( " </SPAN>\n" );
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