document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1185672>Question 1185672</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Mariel and Liu are running a long-distance race. Mariel runs at a rate of 5.4 m/s, and Liu runs at a rate of 7.6 m/s. If Mariel has a 20 m head start, how long will it take for Liu to catch Mariel? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #816521 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=816521\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> mariel funs at a rate of 5.4 meters per second.<BR>\n" );
document.write( "liu runs at a rate of 7.6 meters per second.<BR>\n" );
document.write( "mariel has a 20 meter head start.\r<BR>\n" );
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document.write( "rate * time = distance.\r<BR>\n" );
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document.write( "when liu catches up to mariel, they will have both ran the same time;.<BR>\n" );
document.write( "mariel runs a distance of x.<BR>\n" );
document.write( "liu runs a distance of x + 2-\r<BR>\n" );
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document.write( "the equation for mariel is rate * time = distance becomes 5.4 * T = x<BR>\n" );
document.write( "the equation for liu is rate * time = distance becomes 7.6 * T = x + 20\r<BR>\n" );
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document.write( "solve both equations for T to get:\r<BR>\n" );
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document.write( "T = x/5.4 for mariel.<BR>\n" );
document.write( "T = (x + 20)/7.6 for liu.\r<BR>\n" );
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document.write( "since they're both equal to T, set them equal to each other to getg.\r<BR>\n" );
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document.write( "x/5.4 = (x + 20)/7.6\r<BR>\n" );
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document.write( "cross multiply to get:\r<BR>\n" );
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document.write( "7.6 * x = 5.4 * (x + 20)\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "7.6 * x = 5.4 * x + 108\r<BR>\n" );
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document.write( "subtract 5.4 * x from both sides of the equation to get:\r<BR>\n" );
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document.write( "2.2 * x = 108\r<BR>\n" );
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document.write( "solve for x to get:\r<BR>\n" );
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document.write( "x = 108/2.2 = 49.090909091 meters.\r<BR>\n" );
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document.write( "x + 20 is therefore equal to 69.090909091 meters.\r<BR>\n" );
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document.write( "in 9.090909091 seconds, mariel traveled that * 5.4 meters per second = 49.090909091 meters.\r<BR>\n" );
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document.write( "in 9.090909091 seconds, liu traveled that * 7.6 meters per second = 69.090909091 meters.\r<BR>\n" );
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document.write( "since mariel had a 20 meter headstart, liu caught up to him in 9.090909091 seconds.\r<BR>\n" );
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document.write( "69.090909091 minus 49.090909091 = 20 meters.<BR>\n" );
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document.write( " </SPAN>\n" );
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