document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=958497>Question 958497</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am having a problem setting up an equation for this problem. I keep getting squared variables and I know that's wrong. The problem reads: John recently drove to visit his parents who live 420 miles away on his way there his average speed was 9 miles per hour faster than on his way home if John spent a total of 21 hours driving find the two rates. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #585827 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=585827\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let R1 be his rate going to his parents home and<BR>\n" );
document.write( "R2 be his rate going back to his home, also <BR>\n" );
document.write( "T1 is the time he took going to his parents home and<BR>\n" );
document.write( "T2 is the time he took going back to his home, we are given<BR>\n" );
document.write( "T1 + T2 = 21 hours and<BR>\n" );
document.write( "R1 = R2 + 9<BR>\n" );
document.write( "we use rate times time = distance<BR>\n" );
document.write( "(R2 +9) * T1 = 420 and<BR>\n" );
document.write( "R2 * T2 = 420<BR>\n" );
document.write( "therefore T1 = 420 / (R2+9) and T2 = 420/R2 and we know that<BR>\n" );
document.write( "420/(R2+9) + 420/R2 = 21<BR>\n" );
document.write( "note that the LCD is R2*(R2+9) and we get the following quadratic<BR>\n" );
document.write( "21R2^2 -651R2 -3780 = 0<BR>\n" );
document.write( "we use the quadratic formula to solve but first note that the discriminant is<BR>\n" );
document.write( "square root(b^2 -4*a*c) = square root ((-651)^2 -(4*21*(-3780))) = 861, then<BR>\n" );
document.write( "R2 = (-(-651) + 861) / (2*21)) = 36<BR>\n" );
document.write( "R2 = (-(-651) - 861) / (2*21)) = -5<BR>\n" );
document.write( "we want the positive value for R2, therefore<BR>\n" );
document.write( "R1 = R2 +9 = 36 +9 = 45<BR>\n" );
document.write( "John's rate to his parent's house is 45 mph and his rate back to his home is 36 mph<BR>\n" );
document.write( "  </SPAN>\n" );
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