document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=975934>Question 975934</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Fred originally ran a 42km marathon in 3 hours. Fred wants to improve his net time by six minutes next year. He will try a different strategy of running for the first two hours at a certain (but unknown) speed, and then completing the rest of the race at a rate 2 kilometres per hour faster than this speed.\r<BR>\n" );
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document.write( "If he is to succeed, what is the speed will he need to run for the first two hours of next year’s marathon? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #597626 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=597626\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  Fred originally ran a 42km marathon in 3 hours.<BR>\n" );
document.write( " Fred wants to improve his net time by six minutes next year.<BR>\n" );
document.write( " He will try a different strategy of running for the first two hours at a certain (but unknown) speed, and then completing the rest of the race at a rate 2 kilometres per hour faster than this speed.<BR>\n" );
document.write( "If he is to succeed, what is the speed will he need to run for the first two hours of next year’s marathon?<BR>\n" );
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document.write( "Find the time (in hrs) of his improved time (6 min less than 3 hrs)<BR>\n" );
document.write( "2 + 54/60 = 2.9 hrs<BR>\n" );
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document.write( "Let s = his initial speed<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(s+2) = finishing speed<BR>\n" );
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document.write( "Write a distance equation: dist = time * speed<BR>\n" );
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document.write( "initial speed dist + finishing speed dist = 42 km<BR>\n" );
document.write( "2s + .9(s+2) = 42<BR>\n" );
document.write( "2s + .9s + 1.8 = 42<BR>\n" );
document.write( "2.9s = 42 - 1.8<BR>\n" );
document.write( "2.9s = 40.2<BR>\n" );
document.write( "s = 40.2/2.9<BR>\n" );
document.write( "s = 13.862 km/hr is his initial speed<BR>\n" );
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document.write( "Confirm this by finding the actual dist at each speed.<BR>\n" );
document.write( "2(13.862) = 27.724 km<BR>\n" );
document.write( ".9(15.862) = 14.276 km (2km faster)<BR>\n" );
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document.write( "total dist: 42.000 km </SPAN>\n" );
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