document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=280810>Question 280810</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A motorboat traveling with the current can go 36 miles in 2 hours. against the current it takes 3 hours to go to the same distance. Find the rate of the motorboat in calm water. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #204075 by </B><A HREF=/tutors/aboutme.mpl?userid=oberobic><B>oberobic(2304)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=oberobic><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=204075\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> d = r*t is the basic distance equation.<BR>\n" );
document.write( "s = speed of the motor boat in calm water<BR>\n" );
document.write( "c = speed of current<BR>\n" );
document.write( "s + c = speed of the boat traveling with the current<BR>\n" );
document.write( "s - c = speed of the boat traveling against the current<BR>\n" );
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document.write( "traveling with the current the boat went 36 miles in 2 hrs<BR>\n" );
document.write( "d = 36<BR>\n" );
document.write( "r = s+c<BR>\n" );
document.write( "t = 2<BR>\n" );
document.write( "36 = (s+c)*2 <BR>\n" );
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document.write( "traveling against the current the boat can return 36 miles in 3 hrs<BR>\n" );
document.write( "d = 36<BR>\n" );
document.write( "r = s-c<BR>\n" );
document.write( "t = 3<BR>\n" );
document.write( "36 = (s-c)*3<BR>\n" );
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document.write( "We've got two unknowns and we've got two unknowns, so this can be approached as a system of linear equations.<BR>\n" );
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document.write( "2s + 2c = 36<BR>\n" );
document.write( "3s - 3c = 36<BR>\n" );
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document.write( "Multiply the first equation by 3 and the second by 2 to enable elimination.<BR>\n" );
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document.write( "3(2s + 2c) = 3(36) = 6s + 6c = 108<BR>\n" );
document.write( "2(2s - 2c) = 2(36) = 6s - 6c = 72<BR>\n" );
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document.write( "6s + 6c = 108<BR>\n" );
document.write( "6s - 6c = 72<BR>\n" );
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document.write( "adding them to eliminate the 6c and -6c.<BR>\n" );
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document.write( "12s = 180<BR>\n" );
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document.write( "divide by 12<BR>\n" );
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document.write( "s = 15 = speed of the boat in calm water<BR>\n" );
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document.write( "substituting back into our first equation<BR>\n" );
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document.write( "36 = (s+c)*2 <BR>\n" );
document.write( "2s + 2c = 36<BR>\n" );
document.write( "2(15) + 2c = 36<BR>\n" );
document.write( "2c = 6<BR>\n" );
document.write( "c = 3 = speed of the current<BR>\n" );
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document.write( "checking...<BR>\n" );
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document.write( "traveling with the current, the boat's speed = 15+3 = 18<BR>\n" );
document.write( "to travel 36 miles, it would take 2 hr, which is what the problem stated.<BR>\n" );
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document.write( "traveling against the current, the boat's speed = 15 -3 = 12<BR>\n" );
document.write( "again we can see that to travel the 36 miles it would take 3 hrs, which is also what was stated.<BR>\n" );
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document.write( "Answer:<BR>\n" );
document.write( "s = 15 = speed of the boat in calm water<BR>\n" );
document.write( "c = 3 = speed of the current<BR>\n" );
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document.write( "Done </SPAN>\n" );
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