document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=74813>Question 74813</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0534405991/algebrahomeworkh>College Algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Two ships leave port at the same time. One sails south at 15 mi/h and the other sails east at 20 mi/h. Find the function that models the distance (D) between the ships in terms of the time [(t) in hours] elapsed since their departure. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #53751 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=53751\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is a Pythagorean theorem problem.  The two ships are at the vertex of a right angle. <BR>\n" );
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document.write( "One ship sails east and the distance it is from the starting point is 20*t where t is the time<BR>\n" );
document.write( "that it has been underway.<BR>\n" );
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document.write( "The other ship sails south which is at an angle of 90 degrees to the path of the ship that<BR>\n" );
document.write( "is going east.  The distance that it is from the starting point is 15*t where t is also the<BR>\n" );
document.write( "time that it has been underway.<BR>\n" );
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document.write( "Both of these paths are the legs of a right triangle.  The distance between the ships is<BR>\n" );
document.write( "the hypotenuse of the triangle.<BR>\n" );
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document.write( "The Pythagorean theorem says that the sum of the squares of the two legs of a right triangle<BR>\n" );
document.write( "is equal to the square of the hypotenuse of the triangle. In equation form this would be:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%5E2+%2B+e%5E2+=+D%5E2 ALIGN=MIDDLE  ALT=\"s%5E2+%2B+e%5E2+=+D%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Where s represents the distance to the south of the starting point and e represents<BR>\n" );
document.write( "the distance to the east of the starting point.  D is the distance between the two ships.<BR>\n" );
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document.write( "Substituting the two distances the ships have sailed at time t we get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2815t%29%5E2+%2B+%2820t%29%5E2+=+D%5E2 ALIGN=MIDDLE  ALT=\"%2815t%29%5E2+%2B+%2820t%29%5E2+=+D%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Squaring the terms on the left side results in:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=225t%5E2+%2B+400t%5E2+=+D%5E2 ALIGN=MIDDLE  ALT=\"225t%5E2+%2B+400t%5E2+=+D%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "You can then add the two terms on the left side:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=625t%5E2+=+D%5E2 ALIGN=MIDDLE  ALT=\"625t%5E2+=+D%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Then to solve for D, take the square root of both sides:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28D%5E2%29+=+sqrt%28625t%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28D%5E2%29+=+sqrt%28625t%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "which reduces to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D+=+25t ALIGN=MIDDLE  ALT=\"D+=+25t\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D+=+-25t ALIGN=MIDDLE  ALT=\"D+=+-25t\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "In this case we can ignore the negative solution because a negative distance between<BR>\n" );
document.write( "them really has no meaning.<BR>\n" );
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document.write( "So the distance between the two ships is 25 times the time in hours that the ships have<BR>\n" );
document.write( "been sailing. If they have been moving for 1 hour the distance between them is 25 miles.<BR>\n" );
document.write( "If they have been going for 2 hours, the distance between them is 25*2 = 50 miles.<BR>\n" );
document.write( "And so on ...<BR>\n" );
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document.write( "Hope this helps you to understand the problem. </SPAN>\n" );
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