document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=241558>Question 241558</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If I run my first 60 km lap at a rate 25% faster than my usual 12 km/hr, and my second 60 km lap at a rate ___% slower than 12 km/hr, then my overall average speed will be my usual speed\r<BR>\n" );
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document.write( "A) 50/3   B) 20       C) 25       D) 250/3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #176914 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=176914\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Usual speed is 12 km/hr<BR>\n" );
document.write( "25% faster = 12 + .25*12 = 12*(1+.25) = 12*(1.25) = 15 km/hr<BR>\n" );
document.write( "25% slower = 12 - x*12 = 12*(1-x) km/hr\r<BR>\n" );
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document.write( "first 60 km lap is done at 15 km/hr<BR>\n" );
document.write( "second 60 km lap is done at 12*(1-x) km/hr\r<BR>\n" );
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document.write( "overall average is 12km /hr\r<BR>\n" );
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document.write( "15 * 60 + 12*(1-x) * 60 = 120 * 12\r<BR>\n" );
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document.write( "900 + (12-12x) * 60 = 1440\r<BR>\n" );
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document.write( "900 + 720 - 720*x = 1440\r<BR>\n" );
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document.write( "add 720*x to both sides of the equation and subtract 1440 from both sides to get:\r<BR>\n" );
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document.write( "900 + 720 - 1440 = 720*x\r<BR>\n" );
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document.write( "combine like terms to get:\r<BR>\n" );
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document.write( "1620 - 1440 = 720*x\r<BR>\n" );
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document.write( "combine further to get:\r<BR>\n" );
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document.write( "180 = 720*x\r<BR>\n" );
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document.write( "divide both sides of the equation by 720 to get:\r<BR>\n" );
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document.write( "x = .25\r<BR>\n" );
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document.write( "substitute in the original equation to get:\r<BR>\n" );
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document.write( "15 * 60 + 12*(1-x) * 60 = 120 * 12 becomes:\r<BR>\n" );
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document.write( "15*60 + 12*(1-.25)*60 = 120*12 which becomes:\r<BR>\n" );
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document.write( "900 + 12*.75*60 = 1440 which becomes\r<BR>\n" );
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document.write( "900 + 540 = 1440 which becomes:\r<BR>\n" );
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document.write( "1440 = 1440 which confirms the answer is good.\r<BR>\n" );
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document.write( "answer is:\r<BR>\n" );
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document.write( "x = .25 * 100% = 25%\r<BR>\n" );
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document.write( " </SPAN>\n" );
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