document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=524424>Question 524424</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have been stuck on this one for a while now.  Trying to define variables, write and equation and solve.  Please help me!!\r<BR>\n" );
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document.write( "The distance going up and down a hill is 15 miles.  It takes a total of 2 hours to complete the trip.  Going down the hill is 20 mph faster than going up.  How fast is the trip up the hill in mph? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #347734 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=347734\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The distance going up and down a hill is 15 miles. It takes a total of 2 hours to complete the trip. Going down the hill is 20 mph faster than going up. How fast is the trip up the hill in mph?<BR>\n" );
document.write( "Let y = time (hours) going uphill<BR>\n" );
document.write( "then<BR>\n" );
document.write( "2-y = time (hours) going downhill<BR>\n" );
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document.write( "Let x = speed (mph) going uphill<BR>\n" );
document.write( "then<BR>\n" );
document.write( "x+20 = speed (mph) going downhill<BR>\n" );
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document.write( "applying distance formula of d=rt<BR>\n" );
document.write( "xy = 15 (equation 1)<BR>\n" );
document.write( "(x+20)(2-y) = 15 (equation 2)<BR>\n" );
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document.write( "solving equation 1 for y:<BR>\n" );
document.write( "y = 15/x<BR>\n" );
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document.write( "plug into equation 2 and solve for x:<BR>\n" );
document.write( "(x+20)(2-y) = 15<BR>\n" );
document.write( "(x+20)(2-15/x) = 15<BR>\n" );
document.write( "multiplying both sides by x:<BR>\n" );
document.write( "(x+20)(2x-15) = 15x<BR>\n" );
document.write( "2x^2-15x+40x-300 = 15x<BR>\n" );
document.write( "2x^2+25x-300 = 15x<BR>\n" );
document.write( "2x^2+10x-300 = 0<BR>\n" );
document.write( "x^2+5x-150 = 0<BR>\n" );
document.write( "(x+15)(x-10) = 0<BR>\n" );
document.write( "x = {-15, 10}<BR>\n" );
document.write( "throw out negative solution leaving<BR>\n" );
document.write( "x = 10 mph (speed going up the hill) </SPAN>\n" );
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