document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=335061>Question 335061</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the following by substitution and elimination:\r<BR>\n" );
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document.write( "On a football field during a game, Player A who runs the 40 yard dash in 4.9 seconds catches the ball at his own 30 yard line, then takes off running toward the goal line.  Player B who runs the 40 yard dash in 4.5 seconds is standing on the 25 yard line when Player A catches the ball, he then pursues the ball. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #240211 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=240211\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A runs the 40 yard dash in 4.9 seconds.<BR>\n" );
document.write( "B runs the 40 yard dash in 4.5 seconds.\r<BR>\n" );
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document.write( "Speed of A is equal to 40 / 4.9 yards per second.\r<BR>\n" );
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document.write( "Speed of B is equal to 40 / 4.5 yards per second.\r<BR>\n" );
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document.write( "A catches the ball at his own 30 yard line.\r<BR>\n" );
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document.write( "B is on the 25 yard line when A catches the ball on the 30 yard line.\r<BR>\n" );
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document.write( "In order for B to catch A, he will have to run 5 more yards in the same time as B.\r<BR>\n" );
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document.write( "The basic formula is rate * time = distance.\r<BR>\n" );
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document.write( "The distance that B runs is represented by D.\r<BR>\n" );
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document.write( "The distance that A runs is represented by (D + 5) because A has to run 5 more yards than B in order to catch up to him.\r<BR>\n" );
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document.write( "The time that both runners are traveling is represented by T.\r<BR>\n" );
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document.write( "Since the formula is rate * time = distance, then:\r<BR>\n" );
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document.write( "Formula for A becomes 40/4.9 * T = D\r<BR>\n" );
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document.write( "Formula for B becomes 40/4.5 * T = D + 5\r<BR>\n" );
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document.write( "If we let a = 40/4.9 and we let b = 40/4.5, then:\r<BR>\n" );
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document.write( "Formula for A becomes a * T = D\r<BR>\n" );
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document.write( "Formula for B becomes b * T = D + 5\r<BR>\n" );
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document.write( "We need to solve both these equations simultaneously to get a common answer for both of them.\r<BR>\n" );
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document.write( "If we subtract formula for A from formula for B, then we get:\r<BR>\n" );
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document.write( "b*T - a*T = D+5 - D which becomes:\r<BR>\n" );
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document.write( "b*T - a*T = 5\r<BR>\n" );
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document.write( "Factor out the T to get:\r<BR>\n" );
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document.write( "T * (b-a) = 5\r<BR>\n" );
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document.write( "Divide both sides of this equation by (b-a) to get:\r<BR>\n" );
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document.write( "T = 5 / (b-a)\r<BR>\n" );
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document.write( "Since b = 40/4.5 and a = 40/4.9, this equation becomes:\r<BR>\n" );
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document.write( "T = 5 / (40/4.5 - 40/4.9)\r<BR>\n" );
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document.write( "We use our calculator to solve this to get T = 6.890625 seconds.\r<BR>\n" );
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document.write( "Since A and B are both traveling for the same amount of time, and because rate * time = distance, this means that:\r<BR>\n" );
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document.write( "B has traveled at a rate of 40/4.9 yards per second for 6.890625 seconds = 61.25 yards.\r<BR>\n" );
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document.write( "A has traveled at a rate of 40/4.9 yards per second for 6.890625 seconds = 56.25 yards.\r<BR>\n" );
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document.write( "A started at the 30 yard line and ran for 56.25 yards to get to the 86.25 yard line.\r<BR>\n" );
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document.write( "B started at the 25 yard line and ran for 61.25 yards to get to the 86.25 yard line in the same amount of time.\r<BR>\n" );
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document.write( "B catches up to A at the 86.25 yard line.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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