document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=160302>Question 160302</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0395470560/algebrahomeworkh>Algerbra and Trigonometry structure and method</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> two ships leave port, one sailing east and the other south. Some time later they are 17 miles apart, with the eastbound ship 7 miles further from the port than the southbound ship. how far is each from port? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #118254 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=118254\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> two ships leave port, one sailing east and the other south. Some time later they are 17 miles apart, with the eastbound ship 7 miles further from the port than the southbound ship. how far is each from port?<BR>\n" );
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document.write( "If you look at this, you can see that the hypotenuse of a right triangle is the<BR>\n" );
document.write( "distance between the ships. The two legs are the distance from the ships to port<BR>\n" );
document.write( "A rough diagram will make it easy to understand.<BR>\n" );
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document.write( "Let x = distance of the southbound ship from port<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(x+7) = distance of the eastbound ship from port<BR>\n" );
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document.write( "Hypotenuse = 17 mi<BR>\n" );
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document.write( "x^2 + (x+7)^2 = 17^2<BR>\n" );
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document.write( "FOIL (x+7)(x+7)<BR>\n" );
document.write( "x^2 + (x^2 + 14x + 49) = 289<BR>\n" );
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document.write( "Arrange as a quadratic equation which we can solve:<BR>\n" );
document.write( "x^2 + x^2 + 14x + 49 - 289 = 0<BR>\n" );
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document.write( "2x^2 + 14x - 240 = 0<BR>\n" );
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document.write( "Simplify, divide by 2<BR>\n" );
document.write( "x^2 + 7x - 120 = 0<BR>\n" );
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document.write( "Factor<BR>\n" );
document.write( "(x - 8)(x + 15) = 0<BR>\n" );
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document.write( "Positive solution<BR>\n" );
document.write( "x = 8 mi is southbound ship<BR>\n" );
document.write( "and<BR>\n" );
document.write( "8 + 7 = 15 mi is the eastbound ship<BR>\n" );
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document.write( "Check solution in pythag<BR>\n" );
document.write( "8^2 + 15^2 = 17^2<BR>\n" );
document.write( "64 + 225 = 298<BR>\n" );
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document.write( "Did this make sense? Any questions?<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );