document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=288054>Question 288054</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A----------60m-------------C------40m-------B\r<BR>\n" );
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document.write( "Alphonse starts at point A and runs at a constant rate towards point C. At the same time, Brigitte starts at point B and runs towards point C also at<BR>\n" );
document.write( "a constant rate. They arrive at C at exactly the same moment. If they continue running in the same directions, Alphonse arrives at B exactly 10 seconds before Brigitte arrives at A. How fast was Brigitte running?\r<BR>\n" );
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document.write( "(A) 3 m/s (B) 10/3 m/s (C) 13/3 m/s (D) 5 m/s (E) Not enough information </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #208778 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=208778\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A----------60m-------------C------40m-------B \r<BR>\n" );
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document.write( "Alphonse starts at point A and runs at a constant rate towards point C. At the same time, Brigitte starts at point B and runs towards point C also at<BR>\n" );
document.write( "a constant rate. They arrive at C at exactly the same moment. <BR>\n" );
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document.write( "1st leg:<BR>\n" );
document.write( "Alphonse DATA:<BR>\n" );
document.write( "distance = 60m ; rate = a m/sec ; time = 60/a seconds<BR>\n" );
document.write( "Brigitte DATA:<BR>\n" );
document.write( "distance = 40m ; rate = b m/sec ; time = 40/b seconds<BR>\n" );
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document.write( "1st leg Equation:<BR>\n" );
document.write( "60/a = 40/b<BR>\n" );
document.write( "a = (3/2)b<BR>\n" );
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document.write( "If they continue running in the same directions, Alphonse arrives at B exactly 10 seconds before Brigitte arrives at A. How fast was Brigitte running?<BR>\n" );
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document.write( "Total trip:<BR>\n" );
document.write( "Alphonse DATA:<BR>\n" );
document.write( "distance = 100m ; rate = a m/sec ; time = 100/a m/sec<BR>\n" );
document.write( "Brigitte DATA:<BR>\n" );
document.write( "distance = 100m ; rate = b m/sec ; time = 100/b m/sec<BR>\n" );
document.write( "Total trip Equation:<BR>\n" );
document.write( "Brit time - Alphon time = 10 sec.<BR>\n" );
document.write( "100/b - 100/a = 10 sec<BR>\n" );
document.write( "Multiply thru by ab to get:<BR>\n" );
document.write( "100a - 100b = 10ab<BR>\n" );
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document.write( "Substitute for \"a\" and solve for \"b\":<BR>\n" );
document.write( "100(3/2)b - 100b = 10(3/2)b^2<BR>\n" );
document.write( "(1/2)100b = 15b^2<BR>\n" );
document.write( "15b^2 - 50b = 0<BR>\n" );
document.write( "b(15b-50) = 0<BR>\n" );
document.write( "b = 0 or b = 50/15 = 10/3 <BR>\n" );
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document.write( "Brigitte rate = 10/3 meters/sec<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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document.write( " <BR>\n" );
document.write( "(A) 3 m/s (B) 10/3 m/s (C) 13/3 m/s (D) 5 m/s (E) Not enough information<BR>\n" );
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