document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=503548>Question 503548</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Greetings. <BR>\n" );
document.write( "Anthony Vandorpe here<BR>\n" );
document.write( "I am working on a math word problem in the category of systems of linear equations. \r<BR>\n" );
document.write( "\n" );
document.write( "Here is the general form of the question they gave me:\r<BR>\n" );
document.write( "\n" );
document.write( "there are 2 runners, if they run towards each other, the time elapsed is 12 mins, and the distance is 2 miles presumably they meet at some point in that 2 mile distance).\r<BR>\n" );
document.write( "\n" );
document.write( "If they start running in the same (at the same starting point?) direction, the faster runner will overtake the slower runner in 2 hours.\r<BR>\n" );
document.write( "\n" );
document.write( "This may seem like a simple one to solve, in addition, once I get the 2 linear equations placed in standard form, I am to solve for the variables, and find I think, the running rate of the faster runner and the running rate of the slower runner. I just don't know how to set up this one. I would appreciate your help. Best regards, Anthony C. Vandorpe </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #339285 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=339285\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> there are 2 runners, if they run towards each other, the time elapsed is 12 mins, and the distance is 2 miles presumably they meet at some point in that 2 mile distance).<BR>\n" );
document.write( "----<BR>\n" );
document.write( "1st runner data:<BR>\n" );
document.write( "distance = x miles ; time = 1/6 hr ; rate = distance/time = 6x mph<BR>\n" );
document.write( "---<BR>\n" );
document.write( "2nd runner data:<BR>\n" );
document.write( "distance = 2-x miles ; time = 1/6 hr; rate = distance/time = 12-6x mph<BR>\n" );
document.write( "------------------------------------- <BR>\n" );
document.write( "If they start running in the same (at the same starting point?) direction, the faster runner will overtake the slower runner in 2 hours.<BR>\n" );
document.write( "1st runner data: <BR>\n" );
document.write( "rate = 6x mph ; time = 2 hrs ; distance = rt = 12x miles<BR>\n" );
document.write( "---<BR>\n" );
document.write( "2nd runner data:<BR>\n" );
document.write( "rate = 12-6x mph ; time = 2 hrs ; distance = rt = 24-12x miles<BR>\n" );
document.write( "----------------<BR>\n" );
document.write( "Solve for \"x\":<BR>\n" );
document.write( "distance = distance<BR>\n" );
document.write( "12x = 24-12x<BR>\n" );
document.write( "24x = 24<BR>\n" );
document.write( "x = 1 mile<BR>\n" );
document.write( "--------------------<BR>\n" );
document.write( "You didn't say what the question was but<BR>\n" );
document.write( "with the value of \"x\" you can figure out<BR>\n" );
document.write( "the time and rate for each of the runners.<BR>\n" );
document.write( "==============================================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );