document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=692018>Question 692018</A>: <I><SPAN STYLE=\"word-break: break-all;\"> please help me with this problem. a motorboat with the current went 54mi in 3 hours. against the current, it took 3.6 hours to travel the same distance. find the rate of the boat in calm water and the rate of the current. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #426921 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=426921\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > = rate of the boat in calm water (in miles per hour)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" > = rate of the current (in miles per hour)<BR>\n" );
document.write( " <BR>\n" );
document.write( "With the current, the boat moves at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2Bc ALIGN=MIDDLE  ALT=\"b%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" > miles per hour.<BR>\n" );
document.write( "In <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > hours it covers a distance (in miles) of<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28b%2Bc%29=54 ALIGN=MIDDLE  ALT=\"3%28b%2Bc%29=54\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "Against the current, the boat moves at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b-c ALIGN=MIDDLE  ALT=\"b-c\"   DISABLED_style= \"max-width:90%; height:auto;\" > miles per hour.<BR>\n" );
document.write( "In <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3.6 ALIGN=MIDDLE  ALT=\"3.6\"   DISABLED_style= \"max-width:90%; height:auto;\" > hours it covers a distance (in miles) of<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3.6%28b-c%29=54 ALIGN=MIDDLE  ALT=\"3.6%28b-c%29=54\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "Those two equations form a system of linear equations that needs to be solved for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "but they can be simplified a bit.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28b%2Bc%29=54 ALIGN=MIDDLE  ALT=\"3%28b%2Bc%29=54\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28b%2Bc%29%2F3=54%2F3 ALIGN=MIDDLE  ALT=\"3%28b%2Bc%29%2F3=54%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2Bc=18 ALIGN=MIDDLE  ALT=\"b%2Bc=18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3.6%28b-c%29=54 ALIGN=MIDDLE  ALT=\"3.6%28b-c%29=54\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3.6%28b-c%29%2F3.6=54%2F3.6 ALIGN=MIDDLE  ALT=\"3.6%28b-c%29%2F3.6=54%2F3.6\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b-c=15 ALIGN=MIDDLE  ALT=\"b-c=15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we can write the system as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28b%2Bc=18%2Cb-c=15%29 ALIGN=MIDDLE  ALT=\"system%28b%2Bc=18%2Cb-c=15%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "You can easily solve the system by substitution, or by elimination.<BR>\n" );
document.write( " <BR>\n" );
document.write( "BY ELIMINATION:<BR>\n" );
document.write( "Adding both equations, we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2b=18%2B15 ALIGN=MIDDLE  ALT=\"2b=18%2B15\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2b=33 ALIGN=MIDDLE  ALT=\"2b=33\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2b%2F2=33%2F2 ALIGN=MIDDLE  ALT=\"2b%2F2=33%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28b=16.5%29 ALIGN=MIDDLE  ALT=\"highlight%28b=16.5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substituting that into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2Bc=18%7D%7D%2C+we+get%0D%0A%7B%7B%7B16.5%2Bc=18 ALIGN=MIDDLE  ALT=\"b%2Bc=18%7D%7D%2C+we+get%0D%0A%7B%7B%7B16.5%2Bc=18\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16.5%2Bc-16.5=18-16.5 ALIGN=MIDDLE  ALT=\"16.5%2Bc-16.5=18-16.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28c=1.5%29 ALIGN=MIDDLE  ALT=\"highlight%28c=1.5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "BY SUBSTITUTION:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b-c=15 ALIGN=MIDDLE  ALT=\"b-c=15\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b-c%2Bc=15%2Bc ALIGN=MIDDLE  ALT=\"b-c%2Bc=15%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=15%2Bc ALIGN=MIDDLE  ALT=\"b=15%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substituting <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%2Bc ALIGN=MIDDLE  ALT=\"15%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" > for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2Bc=18 ALIGN=MIDDLE  ALT=\"b%2Bc=18\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%2Bc%2Bc=18 ALIGN=MIDDLE  ALT=\"15%2Bc%2Bc=18\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%2B2c=18 ALIGN=MIDDLE  ALT=\"15%2B2c=18\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%2B2c-18=18-15 ALIGN=MIDDLE  ALT=\"15%2B2c-18=18-15\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2c=3 ALIGN=MIDDLE  ALT=\"2c=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2c%2F2=3%2F2 ALIGN=MIDDLE  ALT=\"2c%2F2=3%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28c=1.5%29 ALIGN=MIDDLE  ALT=\"highlight%28c=1.5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substituting that into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=15%2Bc ALIGN=MIDDLE  ALT=\"b=15%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=15%2B1.5 ALIGN=MIDDLE  ALT=\"b=15%2B1.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28b=16.5%29 ALIGN=MIDDLE  ALT=\"highlight%28b=16.5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );