document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=921183>Question 921183</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi there I'm having trouble solving what I'm sure is a simple equation.  A ship is en route and the present speed is 13.5knots. The time is 9am. The distance yet to travel is 215nautical miles which will give an arrival time of 0055. I want to arrive at 0600 tomorrow not 0055. I want to know when I can reduce my speed to 8kts to arrive at the intended time. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #558835 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=558835\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your current rate of speed is 13.5 knots per hour.<BR>\n" );
document.write( "the distance to be covered is 215 knots.<BR>\n" );
document.write( "you are starting at 9am.\r<BR>\n" );
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document.write( "rate * time = distance<BR>\n" );
document.write( "13.5 * time = 215<BR>\n" );
document.write( "time = 215/13.5 = 15.92592593 hours.\r<BR>\n" );
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document.write( "that will get you into port at approximately 9 + 15.92592593 = 24.92592593 hours from the previous midnight (9am is 9 hours past the previous midnight).\r<BR>\n" );
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document.write( "subtract 24 and you will arrive at approximately .92592593 hours which comes out to be roughly 0:55.5555... the next morning.\r<BR>\n" );
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document.write( "0055 in the morning is close but not quite right on.\r<BR>\n" );
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document.write( "that's not very important to solving this problem, however.\r<BR>\n" );
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document.write( "more importantly, you want to arrive at 6:00 am in the morning and you want to know when you can drop your speed to 8 knots per hour in order to do so.\r<BR>\n" );
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document.write( "in order to arrive at 6:00 am you need to be traveling 21 hours total.\r<BR>\n" );
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document.write( "9 hours past the previous midnight  + 21 = 30 hours past the previous midnight.\r<BR>\n" );
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document.write( "subtract 24 from that and you get 6am the next morning.\r<BR>\n" );
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document.write( "your total travel time needs to be 21 hours.\r<BR>\n" );
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document.write( "let x equal the time you are traveling at 13.5 knots.<BR>\n" );
document.write( "let y equal the time you are traveling at 8 knots.\r<BR>\n" );
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document.write( "you get 2 equations.\r<BR>\n" );
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document.write( "x + y = 21 (first equation)<BR>\n" );
document.write( "13.5x + 8y = 215 (second equation)\r<BR>\n" );
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document.write( "the first equation tells you the total time you traveled.<BR>\n" );
document.write( "the second equation tells you the total distance you traveled.\r<BR>\n" );
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document.write( "you need to solve these equations simultaneously for x and y.\r<BR>\n" );
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document.write( "multiply both sides of the first equation by 8 and you get:\r<BR>\n" );
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document.write( "8x + 8y = 168 (first equation after both sides are multiplied by 8)<BR>\n" );
document.write( "13.5x + 8y = 215 (second equation)\r<BR>\n" );
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document.write( "subtract the second equation form the first to get:\r<BR>\n" );
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document.write( "5.5x = 47\r<BR>\n" );
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document.write( "divide both sides of the equation by 5.5 to get:\r<BR>\n" );
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document.write( "x = 47/5.5 = 470/55 = 94/11\r<BR>\n" );
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document.write( "since x + y = 21, this means that y = 21 - 94/11 = 231/11 - 94/11 = 137/11\r<BR>\n" );
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document.write( "you have:\r<BR>\n" );
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document.write( "x = 94/11<BR>\n" );
document.write( "y = 137/11\r<BR>\n" );
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document.write( "he will travel 94/11 hours at 13.5 knots and 137/11 hours at 8 knots.\r<BR>\n" );
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document.write( "the total distance traveled is 13.5 * 94/11 + 8 * 137/11 = 215 knots.\r<BR>\n" );
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document.write( "the total hours traveled = 94/11 + 137/11 = 21 hours.\r<BR>\n" );
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document.write( "he starts at 9am the previous morning, travels for 21 hours, and arrives at 6am the next morning.\r<BR>\n" );
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document.write( "9 hours past the previous midnight plus 21 hours = 30 hours past the previous midnight equals 30 - 24 = 6 hours part the next midnight which equals 6am the next morning.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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