document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=200406>Question 200406</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A boat took 5 hours to travel 60 kilometers up a river against a current. The return trip took 3 hours .Find the speed of the boat in still water and the speed of the current.\r<BR>\n" );
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document.write( "Solve the linear system\r<BR>\n" );
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document.write( "x-2/3 + y+1/5 = 2\r<BR>\n" );
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document.write( "x+2/7 - y+5/3 = -2\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #150793 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=150793\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A boat took 5 hours to travel 60 kilometers up a river against a current.<BR>\n" );
document.write( " The return trip took 3 hours<BR>\n" );
document.write( " .Find the speed of the boat in still water and the speed of the current.<BR>\n" );
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document.write( "Let x = speed of the boat in still water<BR>\n" );
document.write( "Let y = speed of the current<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(x+y) = speed downstream<BR>\n" );
document.write( "(x-y) = speed upstream<BR>\n" );
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document.write( "Write a dist equation for each trip: Dist = time * speed<BR>\n" );
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document.write( "5(x - y) = 60<BR>\n" );
document.write( "3(x + y) = 60<BR>\n" );
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document.write( "Simplify, divide the 1st equation by 5, and the 2nd equation by 3, results:<BR>\n" );
document.write( "x - y = 12<BR>\n" );
document.write( "x + y = 20<BR>\n" );
document.write( "--------------addition eliminates y, find x<BR>\n" );
document.write( "2x = 32<BR>\n" );
document.write( "x = 16 km/hr boat speed in still water<BR>\n" );
document.write( "and<BR>\n" );
document.write( "16 + y = 20<BR>\n" );
document.write( "y = 20 - 16<BR>\n" );
document.write( "y = 4 km/hr current speed<BR>\n" );
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document.write( "Check solution in original 1st equation<BR>\n" );
document.write( "5(16 - 4) = 60<BR>\n" );
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document.write( "Solve the linear system<BR>\n" );
document.write( "Assume it's<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x-2%29%29%2F3 ALIGN=MIDDLE  ALT=\"%28%28x-2%29%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28y%2B1%29%29%2F5 ALIGN=MIDDLE  ALT=\"%28%28y%2B1%29%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x%2B2%29%29%2F7 ALIGN=MIDDLE  ALT=\"%28%28x%2B2%29%29%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28y%2B5%29%29%2F3 ALIGN=MIDDLE  ALT=\"%28%28y%2B5%29%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > = -2 <BR>\n" );
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document.write( "Get rid of the denominators,<BR>\n" );
document.write( " multiply the 1st eq by 15, results:<BR>\n" );
document.write( "5(x-2) + 3(y+1) = 15(2)<BR>\n" );
document.write( "5x - 10 + 3y + 3 = 30<BR>\n" );
document.write( "5x + 3y - 7 = 30<BR>\n" );
document.write( "5x + 3y = 30 + 7<BR>\n" );
document.write( "5x + 3y = 37<BR>\n" );
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document.write( "Multiply the 2nd equation by 21, results:<BR>\n" );
document.write( "3(x+2) - 7(y+5) = 21(-2)<BR>\n" );
document.write( "3x + 6 - 7y - 35 = -42<BR>\n" );
document.write( "3x - 7y - 29 = - 42<BR>\n" );
document.write( "3x - 7y = -42 + 29<BR>\n" );
document.write( "3x - 7y = -13<BR>\n" );
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document.write( "Multiply the 1st equation by 3:<BR>\n" );
document.write( "15x + 9y = 3(37)<BR>\n" );
document.write( "15x + 9y = 111<BR>\n" );
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document.write( "Multiply the 2nd equation by 5<BR>\n" );
document.write( "15x - 35y = 5(-13)<BR>\n" );
document.write( "15x - 35y = -65<BR>\n" );
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document.write( "Use elimination<BR>\n" );
document.write( "15x + 9y = 111<BR>\n" );
document.write( "15x - 35y = -65<BR>\n" );
document.write( "------------------subtraction eliminate x<BR>\n" );
document.write( "+44y = 176<BR>\n" );
document.write( "y = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=176%2F44 ALIGN=MIDDLE  ALT=\"176%2F44\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "y = 4<BR>\n" );
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document.write( "Use the equation: 5x + 3y = 37 to find x<BR>\n" );
document.write( "5x + 3(4) = 37<BR>\n" );
document.write( "5x + 12 = 37<BR>\n" );
document.write( "5x = 37 - 12<BR>\n" );
document.write( "5x = 25<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25%2F5 ALIGN=MIDDLE  ALT=\"25%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = 5<BR>\n" );
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document.write( "x = 5, y = 4 is the solution<BR>\n" );
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document.write( "Check solution in the 1st original equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28x-2%29%29%2F3 ALIGN=MIDDLE  ALT=\"%28%28x-2%29%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28y%2B1%29%29%2F5 ALIGN=MIDDLE  ALT=\"%28%28y%2B1%29%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%285-2%29%29%2F3 ALIGN=MIDDLE  ALT=\"%28%285-2%29%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%284%2B1%29%29%2F5 ALIGN=MIDDLE  ALT=\"%28%284%2B1%29%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F3 ALIGN=MIDDLE  ALT=\"3%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F5 ALIGN=MIDDLE  ALT=\"5%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 2<BR>\n" );
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