document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=271607>Question 271607</A>: <I><SPAN STYLE=\"word-break: break-all;\"> \"Yolanda and Yoko ran in a 100-yd dash. When Yolanda crossed the finish line, Yoko was 10-yd behind her. The girls then repeated the race, with Yolanda starting 10-yd behind the starting line. If each girl ran at the same rate as before, who won the race? By how many yards?\"\r<BR>\n" );
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document.write( "I am a parent who was trying to help her son with his homework. When working on this problem, I had Yolanda running at 100-yd per hour and Yoko at 90-yd per hour. (Just to make the problem easier to solve) My solution has the girls actually meeting up at the 90-yd line, but then Yolanda overtakes Yoko and still wins the race by 1/10 of a yard. However, my son's teacher told him that the girls ended the second race in a tie. Could someone please help me with this?  Thank You! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #198817 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=198817\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Yolanda and Yoko ran in a 100-yd dash. When Yolanda crossed the finish line, Yoko was 10-yd behind her. The girls then repeated the race, with Yolanda starting 10-yd behind the starting line. If each girl ran at the same rate as before, who won the race? By how many yards?\"\r<BR>\n" );
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document.write( "Let the time taken by both in the first race be t to cover 100 yards and 90 yards by Yolanda and Yoko respectively.\r<BR>\n" );
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document.write( "Speed of Yolanda is 100 /t\r<BR>\n" );
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document.write( "Speed of Yoko is 90/t \r<BR>\n" );
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document.write( "They run at the same speed in the next race.\r<BR>\n" );
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document.write( "What is the time taken by each of them to cover their distance?\r<BR>\n" );
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document.write( "Time taken by yolanda to cover 110 yards  is equal to distance /speed <BR>\n" );
document.write( "= 110/(110/t)<BR>\n" );
document.write( "= 11t/10\r<BR>\n" );
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document.write( "Time taken by Yoko to run 100 yards will be 100/ (90/t)= 10t/9\r<BR>\n" );
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document.write( "10/9 is greater than 11/10 so yolanda is faster.\r<BR>\n" );
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document.write( "Yolanda covered the race in 11t/10 \r<BR>\n" );
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document.write( "In 11t/10 yoko will run 90*(11/10) yards\r<BR>\n" );
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document.write( "90*(11 /10 ) = 99 yards\r<BR>\n" );
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document.write( "So yolanda won by 1 yard. \r<BR>\n" );
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document.write( "This appears logical to me. \r<BR>\n" );
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document.write( " </SPAN>\n" );
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