document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=118425>Question 118425</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Bicyclists A and B leave the same point P at the same time at right angles.  B travels 7 mph faster than A. After 3 hours they are 39 miles apart.  Find the speed of each bicyclists.\r<BR>\n" );
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document.write( "I figured out that the answers are 5 and 12 mph but I can't figure out how to do it algebraically.  If you could help that would be great! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #86543 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=86543\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Bicyclists A and B leave the same point P at the same time at right angles. B travels 7 mph faster than A. After 3 hours they are 39 miles apart. Find the speed of each bicyclists. <BR>\n" );
document.write( "I figured out that the answers are 5 and 12 mph but I can't figure out how to do it algebraically. <BR>\n" );
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document.write( "Bike A DATA:<BR>\n" );
document.write( "Rate = x mph ; Time = 3 hrs ;distance =  rt = 3x miles<BR>\n" );
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document.write( "Bike B DATA;<BR>\n" );
document.write( "Rate = x+7 mph ; Time = 3 hrs ; distance = rt = 3(x+7) miles <BR>\n" );
document.write( "EQUATION:<BR>\n" );
document.write( "Use Pythagoras<BR>\n" );
document.write( "39^2 = (3x)^2 +(3x+21)^2 <BR>\n" );
document.write( "39^2 = 9x^2 + 9x^2+126x+21^1<BR>\n" );
document.write( "18x^2+126x-1080 = 0<BR>\n" );
document.write( "2x^2+14x-120=0<BR>\n" );
document.write( "x^2+7x-60=0<BR>\n" );
document.write( "x = [-7 +- sqrt(49-4*-60)]/2<BR>\n" );
document.write( "x = [-7 + sqrt(289)]/2<BR>\n" );
document.write( "Positive answer:\r<BR>\n" );
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document.write( "x = [-7 + 17]/2<BR>\n" );
document.write( "x = 5 <BR>\n" );
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document.write( "A's rate = 5 mph<BR>\n" );
document.write( "B's rate = 5+7 = 12 mph<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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