document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=297072>Question 297072</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Translate the problem into a pair of linear equations in two variables. Solve the equations using either elimination or substitution. State your answer for the specified variable.\r<BR>\n" );
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document.write( "From a point on a river, two boats are driven in opposite directions, one at 10 miles per hour and the other at 8 miles per hour. In how many hours will they be 54 miles apart? (Points :5)\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #213984 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=213984\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Rate * Time = Distance\r<BR>\n" );
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document.write( "D = 54 miles.\r<BR>\n" );
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document.write( "Total distance is the distance traveled by the first boat plus the distance traveled by the second boat.\r<BR>\n" );
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document.write( "The time traveled by both boats will be the same.\r<BR>\n" );
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document.write( "We call it T.\r<BR>\n" );
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document.write( "the distance traveled by both boats is 54 miles.\r<BR>\n" );
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document.write( "The distance traveled by the first boat is equal to x (we assigned that).\r<BR>\n" );
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document.write( "the distance traveled by the second boat is equal to y (we assigned that also).\r<BR>\n" );
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document.write( "x + y = 54.\r<BR>\n" );
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document.write( "The rate of the first boat is 10 miles an hour.\r<BR>\n" );
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document.write( "the rate of the second boat is 8 miles an hour.\r<BR>\n" );
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document.write( "We have 2 equations that need to be solved simultaneously.\r<BR>\n" );
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document.write( "The first equation is:\r<BR>\n" );
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document.write( "10 * T = x\r<BR>\n" );
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document.write( "the second equation is :\r<BR>\n" );
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document.write( "8 * T = y\r<BR>\n" );
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document.write( "We also know that x + y = 54\r<BR>\n" );
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document.write( "Since x = 10 * T and y = 8 * T, we can susbtitute in the equation of x + y = 54 to get:\r<BR>\n" );
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document.write( "10 * T + 8 * T = 54\r<BR>\n" );
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document.write( "This means that 18 * T = 54 which means that T = 3.\r<BR>\n" );
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document.write( "Substituting for T in our equation gets:\r<BR>\n" );
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document.write( "10 * 3 + 8 * 3 = 54 which becomes 30 + 24 = 54 which becomes 54 = 54 which is true.\r<BR>\n" );
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document.write( "The boats will be 54 miles apart in 3 hours.\r<BR>\n" );
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document.write( "The first boat will have traveled 30 miles in 3 hours at 10 miles per hour.\r<BR>\n" );
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document.write( "The second boat will have traveled 24 miles in 3 hours at 8 miles per hour.\r<BR>\n" );
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document.write( "Since they are going in opposite directions, the total distance between them will be 30 + 24 = 54 miles in 3 hours.\r<BR>\n" );
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