document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1087754>Question 1087754</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Joe and Nancy decide to take a road trip. The first 120 miles of the drive is pretty&#8203; easy, while the last 84 miles of the drive is filled with curves. They drove at an average of 9 miles per hour faster for the first 120 miles of the trip. The entire trip took 3 hours. How fast were Joe and Nancy driving for the first 120 miles of the&#8203; trip?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #702049 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=702049\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let r be the rate for the slower, 84 miles, portion of the trip<BR>\n" );
document.write( "let t1 be the time for the 120 miles portion of the trip and t2 for the 84 miles portion<BR>\n" );
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document.write( "1) t1 + t2 = 3<BR>\n" );
document.write( "2) (r+9)*t1 = 120 and r*t2 = 84<BR>\n" );
document.write( "3) (r+9)*t1 + r*t2 = 120 + 84 = 204<BR>\n" );
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document.write( "expand the left side of equation 3<BR>\n" );
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document.write( "r*t1 + 9*t1 + r*t2 = 204<BR>\n" );
document.write( "r*(t1+t2) +9*t1 = 204 <BR>\n" );
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document.write( "substitute for (t1+t2) by using equation 1)<BR>\n" );
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document.write( "3*r + 9*t1 = 204<BR>\n" );
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document.write( "divide both sides of = by 3<BR>\n" );
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document.write( "4) r + 3*t1 = 68<BR>\n" );
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document.write( "use the equation for t1 from the equations defined at 2)<BR>\n" );
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document.write( "t1 = 120 / (r+9)<BR>\n" );
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document.write( "substitute for t1 in equation 4)<BR>\n" );
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document.write( "r + 3*(120/(r+9)) = 68<BR>\n" );
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document.write( "r^2 +9r +360 = 68 * (r+9)<BR>\n" );
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document.write( "r^2 -59r -252 = 0<BR>\n" );
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document.write( "(r-63)*(r+4) = 0<BR>\n" );
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document.write( "r = 63 and r = -4<BR>\n" );
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document.write( "we reject the negative value for r<BR>\n" );
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document.write( "Joe and Nancy drove 63+9 = 72 miles per hour for the first 120 miles of the&#8203; trip<BR>\n" );
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