document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1205894>Question 1205894</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A and B are running a race.  A has an 84 feet head start when they begin running. <BR>\n" );
document.write( "B runs 12 feet while A covers 8 feet.  Determine distance A runs before B overtakes A.\r<BR>\n" );
document.write( "\n" );
document.write( "Not sure how to solve. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #842997 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=842997\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "(Note to tutor @ikleyn: fix a small error in your response....)<br><BR>\n" );
document.write( "The other tutor shows a perfectly good way to set up and solve the problem.<br><BR>\n" );
document.write( "Here is a very different way to set up and solve the problem.<br><BR>\n" );
document.write( "Over some time interval, B runs 12 feet while A runs 8 feet; in that time interval  B runs 4 feet farther than A.<br><BR>\n" );
document.write( "A is 84 feet ahead of B at the start; the number of time intervals needed for B to overtake A is 84/4 = 21.<br><BR>\n" );
document.write( "So the distances the two of them run before B overtakes A are:<br><BR>\n" );
document.write( "A: 21*8 = 168 feet<BR>\n" );
document.write( "B: 21*12 = 252 feet<br><BR>\n" );
document.write( "ANSWER: (distance A runs before B overtakes him) 168 feet<br><BR>\n" );
document.write( "That same solution formally....<br><BR>\n" );
document.write( "Let x be the number of time intervals in which B runs 12 feet and A runs 8 feet.<br><BR>\n" );
document.write( "12x = distance B runs<BR>\n" );
document.write( "8x = distance A runs<br><BR>\n" );
document.write( "In overtaking A, B runs 84 feet farther than A:<BR>\n" );
document.write( "12x = 8x+84<BR>\n" );
document.write( "4x = 84<BR>\n" );
document.write( "x = 21<br><BR>\n" );
document.write( "ANSWER: the distance A runs is 8x = 168 feet<br><BR>\n" );
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