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" );
document.write( "\n" );
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 #854087 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(53742)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=854087\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "Yolanda and Yoko ran in a 100-yd dash. When Yolanda crossed the finish line, Yoko was 10-yd behind her. <BR>\n" );
document.write( "The girls then repeated the race, with Yolanda starting 10-yd behind the starting line. <BR>\n" );
document.write( "If each girl ran at the same rate as before, who won the race? By how many yards?<BR>\n" );
document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~~\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;In his post, @mananth presented a formal solution.\r<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;This solution is correct and, generally speaking, &nbsp;it is good.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;But this problem admits much simpler mental solution, &nbsp;based on reasoning.\r<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;If you will master it, &nbsp;you will understand the situation much better.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<B>Solution</B>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "According to the problem, Yolanda ran 100 yards in the same time as Yoko ran 90 yards.\r<BR>\n" );
document.write( "\n" );
document.write( "It is the same as to say that Yolanda ran every 10 yards in the same time as Yoko ran every 9 yards.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So, when Yolanda ran 110 yards (11 times 10 yards), Yoko ran 11 times 9 yards, i.e. 99 yards.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "It means, that in the second scenario, Youlanda will finish when Yoko will be 1 yard before the finish line.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Solved mentally and completely in &nbsp;4 &nbsp;lines, &nbsp;making the solution &nbsp;TRANSPARENT \r<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;and understandable/accessible for a &nbsp;4-the grade student\r<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;without using any equations and without using any expressions.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );