document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=356938>Question 356938</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Rachael runs 2 kilometers to a bus stop, and then rides 4.5 km to school. On average the bus is 45 km/hr faster than Rachael's average running speed. If the entire trip takes 25 minutes, how fast does Rachael run? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #254891 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=254891\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Rachael runs 2 kilometers to a bus stop, and then rides 4.5 km to school. On average the bus is 45 km/hr faster than Rachael's average running speed. If the entire trip takes 25 minutes, how fast does Rachael run?<BR>\n" );
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document.write( "Running DATA:<BR>\n" );
document.write( "distance: 2 km ; rate = x km/h ; time = 2/x hrs<BR>\n" );
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document.write( "Bus DATA:<BR>\n" );
document.write( "distance: 4.5 km ; rate = x+45 km/h ; time = 4.5/(x+45) hrs.<BR>\n" );
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document.write( "Equation:<BR>\n" );
document.write( "time + time = 25/60 hr<BR>\n" );
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document.write( "2/x + 4.5/(x+45) = 5/12<BR>\n" );
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document.write( "Multiply thru by 12x(x+45) to get:<BR>\n" );
document.write( "24(x+45) + 12*4.5x = 5x(x+45)<BR>\n" );
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document.write( "24x + 1080 + 54x = 5x^2 + 225x<BR>\n" );
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document.write( "78x + 1080 = 5x^2 + 225x<BR>\n" );
document.write( "5x^2 + 147x - 1080 = 0<BR>\n" );
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document.write( "Positive solution:<BR>\n" );
document.write( "x = 6.0868 km/h (running rate)<BR>\n" );
document.write( "=================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );