document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1060146>Question 1060146</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A runner traveled 3 miles in the same time that a cyclist traveled 10 miles. The speed of the cyclist was 14 mph greater than that of the runner. What was the cyclists speed?\r<BR>\n" );
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document.write( "The answer is supposed to be 20. I have tried everything I can think of but keep coming up with decimals.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #675137 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=675137\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "\"What was the cyclists speed?\" is the ultimate question here. Since it's unknown and we want to find it, let's make\r<BR>\n" );
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document.write( "x = cyclists speed in miles per hour.\r<BR>\n" );
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document.write( "The runner is 14 mph slower than the cyclist, so the runner's speed is x-14 miles per hour.\r<BR>\n" );
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document.write( "We will use the formula\r<BR>\n" );
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document.write( "distance = rate*time\r<BR>\n" );
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document.write( "\"rate\" is another term for \"speed\". In short, \r<BR>\n" );
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document.write( "d = r*t\r<BR>\n" );
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document.write( "The distance for the runner is 3 miles. So d = 3 for the runner. The value of t is unknown. Let's just leave it as t for now.\r<BR>\n" );
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document.write( "So <BR>\n" );
document.write( "d = r*t<BR>\n" );
document.write( "turns into<BR>\n" );
document.write( "3 = (x-14)*t<BR>\n" );
document.write( "after replacing the variables with the expressions set up earlier. \r<BR>\n" );
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document.write( "Similarly, for the cyclist, this equation<BR>\n" );
document.write( "d = r*t<BR>\n" );
document.write( "turns into<BR>\n" );
document.write( "10 = x*t\r<BR>\n" );
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document.write( "We can solve for t in that other equation to get\r<BR>\n" );
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document.write( "10 = x*t<BR>\n" );
document.write( "10/x = t<BR>\n" );
document.write( "t = 10/x\r<BR>\n" );
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document.write( "Then let's plug that into the first equation\r<BR>\n" );
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document.write( "3 = (x-14)*t<BR>\n" );
document.write( "3 = (x-14)*(10/x) ... replace t with 10/x\r<BR>\n" );
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document.write( "Now isolate x\r<BR>\n" );
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document.write( "3 = (x-14)*(10/x)<BR>\n" );
document.write( "3*x = (x-14)*(10/x)*x ... multiply both sides by x<BR>\n" );
document.write( "3x = 10(x-14)<BR>\n" );
document.write( "3x = 10x - 140<BR>\n" );
document.write( "3x - 10x = -140<BR>\n" );
document.write( "-7x = -140<BR>\n" );
document.write( "x = 20 ... divide both sides by -7\r<BR>\n" );
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document.write( "So that's why the cyclist's speed is 20 mph. \r<BR>\n" );
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document.write( "Let me know if this helps or not. Thank you. <BR>\n" );
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