document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1189896>Question 1189896</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two cyclists start at the same point and travel in opposite directions. <BR>\n" );
document.write( "One cyclist travels 3 km faster than the other. <BR>\n" );
document.write( "If the two cyclists are 90 kilometers apart after 2 hours, what is the rate of each cyclist? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #821397 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=821397\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> r = rate for first cyclist.<BR>\n" );
document.write( "r + 3 = rate for second cyclist.<BR>\n" );
document.write( "t = time = 2 hours for both cyclists.<BR>\n" );
document.write( "d = distance for first cyclist.<BR>\n" );
document.write( "90 - d = distance for second cyclisst.\r<BR>\n" );
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document.write( "rate * time = distance formula for first cyclist is r * 2 = d.<BR>\n" );
document.write( "rate * time = distance formula for second cyclist is (r + 3) * 2 = 90 - d\r<BR>\n" );
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document.write( "simplify the second equation to get:<BR>\n" );
document.write( "(r + 3) * 2 = 90 - d becomes:<BR>\n" );
document.write( "r * 2 + 6 = 90 - d<BR>\n" );
document.write( "subtract 6 from both sides of the equation to get:<BR>\n" );
document.write( "r * 2 = 84 - d\r<BR>\n" );
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document.write( "solve for d in both equations to get:<BR>\n" );
document.write( "d = r * 2 for the first cyclist.<BR>\n" );
document.write( "d = 84 - r * 2 for the second cyclist.\r<BR>\n" );
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document.write( "subtract the first equaiton from the second to get:<BR>\n" );
document.write( "0 = 84 - 2 * r * 2<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "0 = 84 - 4 * r<BR>\n" );
document.write( "add 4 * r to both sides of the equation to0 get:<BR>\n" );
document.write( "4 * r = 84<BR>\n" );
document.write( "soolve for r to get:<BR>\n" );
document.write( "r = 21\r<BR>\n" );
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document.write( "your solution will be:<BR>\n" );
document.write( "the rate of the first cyclist is 21 kilometers per hour and the rate of the second cyclist is 24 kilometers per hour.\r<BR>\n" );
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document.write( "to confirm:<BR>\n" );
document.write( "rate * time = distance for the first cyclist is 21 * 2 = 42.<BR>\n" );
document.write( "rate * time = distance for the second cyclist is 24 * 2 = 48.<BR>\n" );
document.write( "since they are traveling in opposite directions, then the distance between them will be 90 kilometers after 2 hours have elapsed.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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