document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=170222>Question 170222</A>: <I><SPAN STYLE=\"word-break: break-all;\"> HELP!!!\r<BR>\n" );
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document.write( "As part of his training, an athlete usually runs 80km at a steady speed of v km/.  One day he decideds to reduce his speed by 2.5km/h and his run takes him an extrax 2h 40 min. Derive an equation in terms of v and use to find athlete's initial speed. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #125657 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=125657\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> As part of his training, an athlete usually runs 80km at a steady speed of v km/. One day he decideds to reduce his speed by 2.5km/h and his run takes him an extrax 2h 40 min. Derive an equation in terms of v and use to find athlete's initial speed.<BR>\n" );
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document.write( "Before change DATA:<BR>\n" );
document.write( "distance = 80km ; rate = v km/h ; time = d/r = 80/v hrs.<BR>\n" );
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document.write( "After change DATA:<BR>\n" );
document.write( "distance = 80km ; rate = (v-2.5)km/h ; time = d/r = 80/(v-2.5) hrs<BR>\n" );
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document.write( "EQUATION:<BR>\n" );
document.write( "After time - Before time = 2 2/3 hr.<BR>\n" );
document.write( "80/(v-2.5) - 80/v = 8/3<BR>\n" );
document.write( "Divide thru by 8 to get:<BR>\n" );
document.write( "10/(v-2.5) - 10/v = 1/3\r<BR>\n" );
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document.write( "Multiply thru with 3v(v-2.5) to get:<BR>\n" );
document.write( "30v - 30(v-2.5) = v(v-2.5)<BR>\n" );
document.write( "2.5 = v^2-2.5v<BR>\n" );
document.write( "v^2-2.5v-2.5 = 0<BR>\n" );
document.write( "v = [2.5 +- sqrt(6.25 - 4*-2.5)]/2<BR>\n" );
document.write( "v = [2.5 +- sqrt(6.25 + 10)]/2<BR>\n" );
document.write( "Positive solution:<BR>\n" );
document.write( "v = [2.5 + 4.03]/2<BR>\n" );
document.write( "v = 3.26556....km/h<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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