document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=166479>Question 166479</A>: <I><SPAN STYLE=\"word-break: break-all;\"> From a point on a river, two boats are driven in opposite directions, one at 5 miles per hour, and the other at 8 miles per hour. In how many hours will they be 52 miles apart?\r<BR>\n" );
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document.write( "(This question is from a sample MET. Thanks very much.) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #122679 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><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=122679\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> D = R * T (distance = rate * time)<BR>\n" );
document.write( "let x = distance boat 1 travels at 5mph in one direction.<BR>\n" );
document.write( "let y = distance boat 2 travels at 8mph in the opposite direction.<BR>\n" );
document.write( "total distance traveled by both boats = 52 miles.<BR>\n" );
document.write( "x + y = 52 (equation 1)<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "boat 1 travels x miles at 5 mph in T hours.<BR>\n" );
document.write( "boat 2 travels y miles at 8 mph in T hours.<BR>\n" );
document.write( "since R * T = D,<BR>\n" );
document.write( "x = 5*T (equation 2)<BR>\n" );
document.write( "y = 8*T (equation 3)<BR>\n" );
document.write( "if you add equation 2 and 3 together, you get<BR>\n" );
document.write( "x + y = 13*T (equation 4)<BR>\n" );
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document.write( "you have 2 equations that you need to solve simultaneously.  they are:<BR>\n" );
document.write( "x + y = 52 (equation 1)<BR>\n" );
document.write( "x + y = 13*T (equation 4)<BR>\n" );
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document.write( "subtract equation 1 from equation 4:<BR>\n" );
document.write( "you get:<BR>\n" );
document.write( "0 = 13*T - 52<BR>\n" );
document.write( "add 52 to both sides:<BR>\n" );
document.write( "52 = 13*T<BR>\n" );
document.write( "divide both sides by 13:<BR>\n" );
document.write( "T = 4<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "they will be 52 miles apart in 4 hours.<BR>\n" );
document.write( "to prove, substitute in equations 2 and 3:<BR>\n" );
document.write( "x = 5*4 = 20 miles<BR>\n" );
document.write( "y = 8*4 = 32 miles<BR>\n" );
document.write( "20 + 32 = 52<BR>\n" );
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document.write( "answer is proven.<BR>\n" );
document.write( "they are 52 miles apart in 4 hours.<BR>\n" );
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