document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1127535>Question 1127535</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Leaving from the same starting line at the same time, Tracy jogs along the riverbank at a constant speed, while Joe paddles a canoe at a constant speed in the river beside her. If Joe was in still water, his speed would be the same as Tracy, but Joe is paddling against a 2 mile per hour current. If Tracy arrives at the end of her 6-mile jog 1 hour before Joe arrives at the same finish line, how fast was Tracy jogging? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #743958 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=743958\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> basic formula to use is rate * time = distance.<BR>\n" );
document.write( "let R = rate and T = time and 6 = D\r<BR>\n" );
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document.write( "formula for tracy becomes RT = 6\r<BR>\n" );
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document.write( "formula for joe becomes (R - 2) * (T + 1) = 6\r<BR>\n" );
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document.write( "simplify the formula for joe to get RT + R - 2T - 2 = 6\r<BR>\n" );
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document.write( "since RT = 6 from the formula for tracy, then the formula for joe becomes 6 + R - 2T - 2 = 6 after you replace RT with 6.\r<BR>\n" );
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document.write( "subtract 6 from both sides of this equation to get 6 + R - 2T - 2 - 6 = 0\r<BR>\n" );
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document.write( "combine like terms to get R - 2T - 2 = 0\r<BR>\n" );
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document.write( "add 2T + 2 to both sides of the equation to get R - 2T - 2 + 2T + 2 = 2T + 2\r<BR>\n" );
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document.write( "combine like terms to get R = 2T + 2\r<BR>\n" );
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document.write( "raplace R with 2T + 2 in the formula for tracy to get (2T + 2) * T = 6\r<BR>\n" );
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document.write( "simplify and subtract 6 from both sides of the equation to get 2T^2 + 2T - 6 = 6 - 6\r<BR>\n" );
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document.write( "combine like terms to get 2T^2 + 2T - 6 = 0\r<BR>\n" );
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document.write( "divide both sides of the equation by 2 to get T^2 + T - 3 = 0\r<BR>\n" );
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document.write( "factor this quadratic equation to get T = -2.302775638 or T = 1.302775638.\r<BR>\n" );
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document.write( "since T can't be negative, then T has to be 1.302775638.\r<BR>\n" );
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document.write( "the formula for tracy becomes R * 1.302775638 = 6.\r<BR>\n" );
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document.write( "solve for R to get R = 6 / 1.302775638 = 4.605551275\r<BR>\n" );
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document.write( "confirm the original formulas are true with these values for T and R.\r<BR>\n" );
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document.write( "R * T = 6 becomes 4.605551275 * 1.302775638 = 6 which becomes 6 = 6, which is true.\r<BR>\n" );
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document.write( "(R - 2) * (T + 1) = 6 becomes 2.605551275 * 2.302775638 = 6 which becomes 6 = 6, which is also true.\r<BR>\n" );
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document.write( "the rate of speed of tracy is the same as the rate of speed of joe in still water, which is 4.605551275 miles per hour.\r<BR>\n" );
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document.write( "tracy jogs the 6 miles in 1.302775638 hours.\r<BR>\n" );
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document.write( "because joe is paddling against a 2 mile per hour current, than joe's net speed is 2.605551275 miles per hour and it takes him 2.302775638 hours to get to the 6 miles mark.\r<BR>\n" );
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document.write( "since tracy takes 1.302775638 hours to get to the 6 mile mark, she takes 1 hour less than joe.\r<BR>\n" );
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document.write( "the requirements of the problem are satisfied.\r<BR>\n" );
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document.write( "the solution is that tracy was jogging at 4.605551275 miles per hour.\r<BR>\n" );
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document.write( "you may round your answer as required.\r<BR>\n" );
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document.write( "the quadratic equation couldn't be factored so i had to resort to the use of the quadratic formula.\r<BR>\n" );
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document.write( "the quadratic formula is:\r<BR>\n" );
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document.write( "            -b plus or minus sqrt(b^2-4ac)\r\n" );
document.write( "     T =   -----------------------------------\r\n" );
document.write( "                           2a\r\n" );
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document.write( "the equation to solve was T^2 + T - 3 = 0\r<BR>\n" );
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document.write( "a is the coefficient of the T^2 term which is equal to 1.<BR>\n" );
document.write( "b is the coefficient of the T term which is equal to 1.<BR>\n" );
document.write( "c is the constant term which is equal to -3.\r<BR>\n" );
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document.write( "plug these in the formula and you get:\r<BR>\n" );
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document.write( "            -b plus or minus sqrt(b^2-4ac)\r\n" );
document.write( "     T =   -----------------------------------\r\n" );
document.write( "                           2a\r\n" );
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document.write( "becomes:\r\n" );
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document.write( "            -1 plus or minus sqrt(1^2-4*1*-3)\r\n" );
document.write( "     T =   -----------------------------------\r\n" );
document.write( "                           2*1\r\n" );
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document.write( "which becomes:\r\n" );
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document.write( "           -1 plus or minus sqrt(13))\r\n" );
document.write( "     T =   -----------------------------------\r\n" );
document.write( "                           2\r\n" );
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document.write( "this results in T = 1.302775638 or T = -2.302775638.\r<BR>\n" );
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document.write( "T has to be positive, so T = 1.302775638.\r<BR>\n" );
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document.write( "the rest of the problem was already solved above.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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