document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=112722>Question 112722</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the word problem i am having trouble completing has different distances, and that is where i get confused. Thank you so much, in advance\r<BR>\n" );
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document.write( "A cyclist travels 20 miles in the same amount of time as it takes a hiker to walk 6 miles. The rate of the cyclist is 7 mph faster than the rate of the hiker. Find the rate of the cyclist and the rate of the hiker. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #82180 by </B><A HREF=/tutors/aboutme.mpl?userid=ptaylor><B>ptaylor(2198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ptaylor><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=ptaylor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=82180\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> ---EVEN THOUGH THE DISTANCES ARE DIFFERENT, THE TIMES ARE THE SAME AND THAT GIVES US THE BASIS FOR SETTING UP AN EQUATION.\r<BR>\n" );
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document.write( "Distance(d) equals Rate(r) times Time(t) or d=rt; r=d/t and t=d/r\r<BR>\n" );
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document.write( "Let r=rate of the hiker\r<BR>\n" );
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document.write( "Then r+7=rate of the cyclist\r<BR>\n" );
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document.write( "time for the hiker=6/r<BR>\n" );
document.write( "time for the cyclist=20/(r+7)\r<BR>\n" );
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document.write( "And we are told that the above two times are the same. So:\r<BR>\n" );
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document.write( "6/r=20/(r+7)  multiply each term by r(r+7)\r<BR>\n" );
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document.write( "6(r+7)=20r  get rid of parens\r<BR>\n" );
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document.write( "6r+42=20r  subtract 6r from both sides\r<BR>\n" );
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document.write( "6r-6r+42=20r-6r collect like terms<BR>\n" );
document.write( "14r=42  divide both sides by 14\r<BR>\n" );
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document.write( "r=3 mph-------------------------rate of the hiker\r<BR>\n" );
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document.write( "r+7=3+7=10 mph------------------rate of the cyclist\r<BR>\n" );
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document.write( "CK\r<BR>\n" );
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document.write( "time for hiker=6/3=2 hrs<BR>\n" );
document.write( "time for cyclist=20/10=2 hrs\r<BR>\n" );
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document.write( "Hope this helps---ptaylor\r<BR>\n" );
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document.write( " </SPAN>\n" );
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