document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=10887>Question 10887</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi,  I am very confused with this problem I cannot seem to apply the pythagoream formula to it.  Can you Please help? Thanks:\" Two boats leave San Diego at the same time.  One boat sails due north and the other due west.  When they are 10 miles apart, the boat traveling north has sailed 2 miles farther than the boat sailing west.  Find the distance each boat has traveled.\" </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #5732 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=5732\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Ok, let the distance traveled by the west-going boat = x miles.  Then the distance traveled by the north-going boat is (x+2) miles.\r<BR>\n" );
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document.write( "You can apply the Pythagorean theorem to this problem.\r<BR>\n" );
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document.write( "In the right triangle you get when you diagram the paths of these two boats, the hypotenuse is their distance from each other and that is 10 miles. So, c = 10 miles.  Now you can set up the equation per Pythagorus: {{c^2 = a^2 + b^2}}}\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%5E2+=+x%5E2+%2B+%28x%2B2%29%5E2 ALIGN=MIDDLE  ALT=\"10%5E2+=+x%5E2+%2B+%28x%2B2%29%5E2\"   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=100+=+x%5E2+%2B+%28x%5E2+%2B+4x+%2B+4%29 ALIGN=MIDDLE  ALT=\"100+=+x%5E2+%2B+%28x%5E2+%2B+4x+%2B+4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify. Subtact 100 from both sides and collect like-terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2+%2B+4x+-+96+=+0 ALIGN=MIDDLE  ALT=\"2x%5E2+%2B+4x+-+96+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor out a 2 to simplify this.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+2x+-+48+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+2x+-+48+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor this quadratic equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+6%29%28x+%2B+8%29+=+0 ALIGN=MIDDLE  ALT=\"%28x+-+6%29%28x+%2B+8%29+=+0\"   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=x+-+6+=+0 ALIGN=MIDDLE  ALT=\"x+-+6+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+6 ALIGN=MIDDLE  ALT=\"x+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" > or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+8+=+0 ALIGN=MIDDLE  ALT=\"x+%2B+8+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-8 ALIGN=MIDDLE  ALT=\"x+=+-8\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Discard this solution as the distance can't be negative.\r<BR>\n" );
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document.write( "So, x = 6 miles and x+2 = 8 miles.\r<BR>\n" );
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document.write( "The north-going boat traveled 8 miles while the west-going boat traveled 6 miles. \r<BR>\n" );
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document.write( "You can see that 6, 8, and 10 are \"Pythagorean numbers becuase <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%5E2+%2B+8%5E2+=+10%5E2 ALIGN=MIDDLE  ALT=\"6%5E2+%2B+8%5E2+=+10%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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