document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1187574>Question 1187574</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello there. I need some help with the following word problem please and thank you in advance! \r<BR>\n" );
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document.write( "Rob Gronowski of the New England Patriots can run 100 yards in 12 seconds, and Matt Forte of the New York Jets can run 100 yards in 9 seconds. Suppose that Gronowski catches a pass at his own 20-yard line in stride and starts running away from Forte, who is at the 15-yard line directly behind Gronowski. At what yard line will Forte catch up to Gronowski?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #818591 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=818591\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> rate * time = distance.\r<BR>\n" );
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document.write( "for rob, the formula becomes r * 12 = 100 yards.<BR>\n" );
document.write( "for matt, the formula becomes r * 9 = 100 yards.\r<BR>\n" );
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document.write( "solve for r to get:\r<BR>\n" );
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document.write( "for rob, r = 100/12.<BR>\n" );
document.write( "for matt, r = 100/9.\r<BR>\n" );
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document.write( "rob catches a pass at his own 20 yard line.<BR>\n" );
document.write( "matt is at the 15 yard line directly behind rob.\r<BR>\n" );
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document.write( "in order to catch rob, matt has to run 5 more yards than rob in the same amount of time.\r<BR>\n" );
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document.write( "let the distance that rob has to run equal to x.<BR>\n" );
document.write( "let the distance that matt has to run equal to x + 5.<BR>\n" );
document.write( "the time is the same for both.\r<BR>\n" );
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document.write( "the formula for rob becomes 100/12 * t = x<BR>\n" );
document.write( "the formula for matt becomes 100/9 * t = x + 5\r<BR>\n" );
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document.write( "subtract the first equation from the second to get:\r<BR>\n" );
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document.write( "100/9 * t - 100/12 * t = 5.\r<BR>\n" );
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document.write( "multiply both sides of this equation by (9 * 12) to get:\r<BR>\n" );
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document.write( "100*12 * t - 100 * 9 * t = 5 * 9 * 12\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "1200 * t - 900 * t = 540\r<BR>\n" );
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document.write( "combine like terms to get:\r<BR>\n" );
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document.write( "300 * t = 540\r<BR>\n" );
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document.write( "divide both sides of the equation by 300 to get:\r<BR>\n" );
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document.write( "t = 540 / 300 = 1.8\r<BR>\n" );
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document.write( "matt will catch up with rob in 1.8 seconds.\r<BR>\n" );
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document.write( "rob starts at the 20 yard line and runs at the rate of 100/12 yards per second for 1.8 seconds.\r<BR>\n" );
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document.write( "100/12 * 1.8 = rate * time = a distance of 15 yards.<BR>\n" );
document.write( "since he starts at the 20 yard line, he winds up at the 35 yard line.\r<BR>\n" );
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document.write( "matt starts at the 15 yard line and runs at the rate of 100/9 yards per second for 1.8 seconds.\r<BR>\n" );
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document.write( "100/9 * 1.8 = rate * time = a distance of 20 yards.<BR>\n" );
document.write( "since he starts at the 15 yard line, he winds up at the 35 yard line.\r<BR>\n" );
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document.write( "the 35 yard line is where matt catches up with rob.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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