document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1046879>Question 1046879</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A boat travels 80 km downstream in 2.5 hours. It travels 50 km upstream in the same length of time. what is the speed of the boat in still water and of the current?\r<BR>\n" );
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document.write( "Thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #662329 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39623)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=662329\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is too common a type of question so I will begin to answer purely in symbols.  Your boat is able to move faster going downstream, but if in still water, assigning the rate or speed r.\r<BR>\n" );
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document.write( "               SPEED         TIME        DISTANCE\r\n" );
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document.write( "DOWNSTR        r+c            t           D\r\n" );
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document.write( "UPSTRM         r-c            t           d\r\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28VARIABLES%2CGIVEN%2CD=80%2Cd=50%2Ct=2.5%2CUNKNOWNS%2Cr=boatStillWater%2Cc=current%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28t%28r%2Bc%29=D%2Ct%28r-c%29=d%29 ALIGN=MIDDLE  ALT=\"system%28t%28r%2Bc%29=D%2Ct%28r-c%29=d%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >-------two equations in two unknown variables; the others are given and constant knowns.<BR>\n" );
document.write( "Solve for c and r.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28tr%2Btc=D%2Ctr-tc=d%29 ALIGN=MIDDLE  ALT=\"system%28tr%2Btc=D%2Ctr-tc=d%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tc=D-tr ALIGN=MIDDLE  ALT=\"tc=D-tr\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=%28D-tr%29%2Ft ALIGN=MIDDLE  ALT=\"c=%28D-tr%29%2Ft\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tr-t%28%28D-tr%29%2Ft%29=d ALIGN=MIDDLE  ALT=\"tr-t%28%28D-tr%29%2Ft%29=d\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tr-%28D-tr%29=d ALIGN=MIDDLE  ALT=\"tr-%28D-tr%29=d\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tr-D%2Btr=d ALIGN=MIDDLE  ALT=\"tr-D%2Btr=d\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2tr-D=d ALIGN=MIDDLE  ALT=\"2tr-D=d\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2tr=d%2BD ALIGN=MIDDLE  ALT=\"2tr=d%2BD\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28r=%28d%2BD%29%2F%282t%29%29 ALIGN=MIDDLE  ALT=\"highlight%28r=%28d%2BD%29%2F%282t%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >-------formula for the still-water speed\r<BR>\n" );
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document.write( "Note, I used substitution, but Elimination might be a possible choice to use.  Elimination being used in finding c, next.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=tr%2Btc-%28tr-tc%29=D-d ALIGN=MIDDLE  ALT=\"tr%2Btc-%28tr-tc%29=D-d\"   DISABLED_style= \"max-width:90%; height:auto;\" > just subtraction corresponding members of the two equations of the system<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2tc=%28D-d%29 ALIGN=MIDDLE  ALT=\"2tc=%28D-d%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which immediately seems more efficient a method...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28c=%28D-d%29%2F%282t%29%29 ALIGN=MIDDLE  ALT=\"highlight%28c=%28D-d%29%2F%282t%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >------river current speed\r<BR>\n" );
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document.write( "---<BR>\n" );
document.write( "AFTER-THOUGHT\r<BR>\n" );
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document.write( "A better way, nearly the same as I showed, would be, fill-in the table with the ACTUAL values first, and of course the UNKNOWN variables too, AND THEN make the generalizations for ALL THE GIVEN VALUES.  Now make a new table, but use only variables for everything.  \r<BR>\n" );
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document.write( "NOW you can more comfortably write your system of equations, and keep in mind which variables are the unknowns.  Solve this system purely in variables.  You will have formulas for each unknown variable from that. </SPAN>\n" );
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