document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1207802>Question 1207802</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a 100-meter race,Todd crosses the finish line 5 meters ahead of Scott. To even things up, Todd suggests to Scott that they race again, this time with Todd lining up 5 meters behind the start. \r<BR>\n" );
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document.write( "(a) Assuming that Todd and Scott run at the same pace as before, does the second race end in a tie? \r<BR>\n" );
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document.write( "(b) If not, who wins? \r<BR>\n" );
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document.write( "(c) By how many meters does he win? \r<BR>\n" );
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document.write( "(d) How far back should Todd start so that the race ends in a tie? \r<BR>\n" );
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document.write( "After running the race a second time, Scott, to even things up, suggests to Todd that he (Scott) line up 5 meters in front of the start. \r<BR>\n" );
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document.write( "(e) Assuming again that they run at the same pace as in the first race, does the third race result in a tie? \r<BR>\n" );
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document.write( "(f) If not, who wins? \r<BR>\n" );
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document.write( "(g) By how many meters? (h) How far ahead should Scott start so that the race ends in a tie?\r<BR>\n" );
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document.write( "Thank you everyone for your help with word problems. Sorry for the many questions buy I truly want to increase my math skills.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #845908 by </B><A HREF=/tutors/aboutme.mpl?userid=mananth><B>mananth(16946)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mananth><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=mananth><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=845908\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In a 100-meter race,Todd crosses the finish line 5 meters ahead of Scott. To even things up, Todd suggests to Scott that they race again, this time with Todd lining up 5 meters behind the start.\r<BR>\n" );
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document.write( "Let Todd's time be t  (s)<BR>\n" );
document.write( "Todd's  speed  will be 100/t     (m/  s)\r<BR>\n" );
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document.write( "In the same time Scott runs 95 m<BR>\n" );
document.write( "Scott's speed = 95/t \r<BR>\n" );
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document.write( "Re run<BR>\n" );
document.write( "Now todd runs  105 m<BR>\n" );
document.write( "Scott runs 100m <BR>\n" );
document.write( "Todd's time = 105/ (100/t) = 105t/100   = 1.05t  (s)\r<BR>\n" );
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document.write( "Scott's time = 100/(95/t)= 100t/95  =1.0526\r<BR>\n" );
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document.write( "Assuming that Todd and Scott run at the same pace as before, does the second race end in a tie?<BR>\n" );
document.write( "No\r<BR>\n" );
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document.write( "(b) If not, who wins?\r<BR>\n" );
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document.write( "Todd\r<BR>\n" );
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document.write( "(c) By how many meters does he win?\r<BR>\n" );
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document.write( "Scott's distance = 1.0526 t*95/t = 99.997 m you find the difference\r<BR>\n" );
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document.write( "(d) How far back should Todd start so that the race ends in a tie?\r<BR>\n" );
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document.write( "The time they reach should be same with different start line<BR>\n" );
document.write( "If Todd runs 100+x meters and Scott  100 meters, their times should be same<BR>\n" );
document.write( "t= d/r<BR>\n" );
document.write( "Todd's time =Scott's time<BR>\n" );
document.write( "(100+x)/(100/t) = 100/(95/t)\r<BR>\n" );
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document.write( "(100+x)t/100 = 100t/95\r<BR>\n" );
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document.write( "Divide by t<BR>\n" );
document.write( "(100+x)/100 = 100/95<BR>\n" );
document.write( "95(100+x) = 100*100<BR>\n" );
document.write( "9500 +95x = 10000<BR>\n" );
document.write( "95x = 500<BR>\n" );
document.write( "x = 500/95 = 5.263 m<BR>\n" );
document.write( "Todd should start about 5.2632 meters behind the start line  to end in a tie.\r<BR>\n" );
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