document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1054995>Question 1054995</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a traveller walks a certain distance. Had he gone half km an hour faster, he would have walked it in four fifth of the time; had he gone half a km an hour slower, he would had been 2.5 hours longer on the road. Find the distance </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #670256 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=670256\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you've got 3 equations that need to be solved simultaneously.\r<BR>\n" );
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document.write( "they are:\r<BR>\n" );
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document.write( "R * T = D\r<BR>\n" );
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document.write( "(R + 1/2) * (4/5 * T) = D\r<BR>\n" );
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document.write( "(R - 1/2) * (T + 2.5) = D\r<BR>\n" );
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document.write( "since all expressions on the left side of each equation are all equal to D, they can all be set equal to each other.\r<BR>\n" );
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document.write( "since R * T is easier to deal with, we'll use that as one of the equal pairs.\r<BR>\n" );
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document.write( "start with:\r<BR>\n" );
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document.write( "R * T = (R + 1/2) * (4/5 * T)\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "R * T = 4/5 * R * T + 1/2 * 4/5 * T\r<BR>\n" );
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document.write( "divide both sides of this equation by T to get:\r<BR>\n" );
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document.write( "R = 4/5 * R + 1/2 * 4/5\r<BR>\n" );
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document.write( "subtract 4/5 * R from both sides of this equation to get:\r<BR>\n" );
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document.write( "R - 4/5 * R = 4/10\r<BR>\n" );
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document.write( "combine like terms to get:\r<BR>\n" );
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document.write( "1/5 * R = 4/10\r<BR>\n" );
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document.write( "multiply both sides of this equation by 5 to get:\r<BR>\n" );
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document.write( "R = 20/10 = 2\r<BR>\n" );
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document.write( "now use R * T = D and (R - 1/2) * (T + 2.5) = D\r<BR>\n" );
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document.write( "set them equal to each other to get:\r<BR>\n" );
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document.write( "R * T = (R - 1/2) * (T + 2.5)\r<BR>\n" );
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document.write( "replace R with 2 to get:\r<BR>\n" );
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document.write( "2 * T = 3/2 * (T + 2.5)\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "2 * T = 3/2 * T + 3/2 * 2.5\r<BR>\n" );
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document.write( "subtract 3/2 * T from both sides of this equation to get:\r<BR>\n" );
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document.write( "1/2 * T = 3/2 * 2.5\r<BR>\n" );
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document.write( "multiply both sides of this equation by 2 to get:\r<BR>\n" );
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document.write( "T = 3 * 2.5 which results in T = 7.5\r<BR>\n" );
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document.write( "you have R = 2 and T = 7.5\r<BR>\n" );
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document.write( "R * T = D becomes 2 * 7.5 = D which results in D = 15.\r<BR>\n" );
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document.write( "(R + 1/2) * (4/5 * T) = D becomes 2.5 * 4/5 * 7.5 = D which becomes 2.5 * 30 / 5 = D which becomes 2.5 * 6 = D which results in D = 15.\r<BR>\n" );
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document.write( "(R - 1/2) * (T + 2.5) = D becomes 3/2 * 10 = D which results in D = 15.\r<BR>\n" );
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document.write( "all 3 equations are satisfied when R = 2 and T = 7.5.\r<BR>\n" );
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document.write( "your solution is that the distance is 15 kilometers.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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