document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=112443>Question 112443</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I had a word problem on a test involving Matrices, determinants and Cramer's Rule. I looked through all of my notes, and did not see anything on word problems and the text book was very vague. My professor created the test himself. We were to use a system to solve this word problem:\r<BR>\n" );
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document.write( "A boat on a river travels downstream between two points, 20 miles apart, in one hour. The return trip against the current takes 2.5 hours. What is the speed of the current of the river?\r<BR>\n" );
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document.write( "My Answer:\r<BR>\n" );
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document.write( "x - 20y = 1<BR>\n" );
document.write( "x + 20y = 2.5\r<BR>\n" );
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document.write( "Using elimination of the y-term 2x = 3.5<BR>\n" );
document.write( "                                 x = 3.5/2\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #82032 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=82032\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'm confused in your analysis, what is x and what is y?<BR>\n" );
document.write( "For these types of problems, start with the following. <BR>\n" );
document.write( "Rate x Time = Distance<BR>\n" );
document.write( "In your problem, the distance is constant at 20 miles. <BR>\n" );
document.write( "When the boat travels downstream, its total rate,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5Bd%5D ALIGN=MIDDLE  ALT=\"R%5Bd%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > is equal to the rate in still water,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5Bb%5D ALIGN=MIDDLE  ALT=\"R%5Bb%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, plus the river rate<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5Br%5D ALIGN=MIDDLE  ALT=\"R%5Br%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "So the equation downstream is <BR>\n" );
document.write( "Rate x Time = Distance<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5Bd%5D+%281%29=20 ALIGN=MIDDLE  ALT=\"R%5Bd%5D+%281%29=20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28R%5Bb%5D%2BR%5Br%5D%29%281%29=20 ALIGN=MIDDLE  ALT=\"%28R%5Bb%5D%2BR%5Br%5D%29%281%29=20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5Bb%5D%2BR%5Br%5D=20 ALIGN=MIDDLE  ALT=\"R%5Bb%5D%2BR%5Br%5D=20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "When the boat travels upstream, its total rate,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5Bu%5D ALIGN=MIDDLE  ALT=\"R%5Bu%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > is equal to the rate in still water,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5Bb%5D ALIGN=MIDDLE  ALT=\"R%5Bb%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, minus the river rate<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5Br%5D ALIGN=MIDDLE  ALT=\"R%5Br%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "So the equation downstream is <BR>\n" );
document.write( "Rate x Time = Distance<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5Bu%5D+%282.5%29=20 ALIGN=MIDDLE  ALT=\"R%5Bu%5D+%282.5%29=20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28R%5Bb%5D-R%5Br%5D%29%282.5%29=20 ALIGN=MIDDLE  ALT=\"%28R%5Bb%5D-R%5Br%5D%29%282.5%29=20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5Bb%5D-R%5Br%5D=8 ALIGN=MIDDLE  ALT=\"R%5Bb%5D-R%5Br%5D=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 2.5.<BR>\n" );
document.write( "1.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5Bb%5D%2BR%5Br%5D=20 ALIGN=MIDDLE  ALT=\"R%5Bb%5D%2BR%5Br%5D=20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5Bb%5D-R%5Br%5D=8 ALIGN=MIDDLE  ALT=\"R%5Bb%5D-R%5Br%5D=8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Adding equation 1 to equation 2 yields,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2R%5Bb%5D=28 ALIGN=MIDDLE  ALT=\"2R%5Bb%5D=28\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5Bb%5D=14 ALIGN=MIDDLE  ALT=\"R%5Bb%5D=14\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and from equation 1,<BR>\n" );
document.write( "1.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5Bb%5D%2BR%5Br%5D=20 ALIGN=MIDDLE  ALT=\"R%5Bb%5D%2BR%5Br%5D=20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=14%2BR%5Br%5D=20 ALIGN=MIDDLE  ALT=\"14%2BR%5Br%5D=20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5Br%5D=6 ALIGN=MIDDLE  ALT=\"R%5Br%5D=6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The rate of the boat in still water is 14 mph. <BR>\n" );
document.write( "The river moves at a rate of 6 mph. <BR>\n" );
document.write( "Hope it helps.  </SPAN>\n" );
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