document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=255326>Question 255326</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A boat traveled 45km downstream in 3 hours. The return trip against the current took 5 hours. Find the rate of the boat in calm water and the rate of the current. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #187608 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=187608\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> b = speed of the boat in calm water<BR>\n" );
document.write( "c = speed of the current flowing downstream<BR>\n" );
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document.write( "The typical distance equation is:  d = rt, where<BR>\n" );
document.write( "d = distance<BR>\n" );
document.write( "r = rate<BR>\n" );
document.write( "t = time<BR>\n" );
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document.write( "Given d = rt, we can rearrange the equation as may be needed:<BR>\n" );
document.write( "r = d/t<BR>\n" );
document.write( "t = d/r<BR>\n" );
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document.write( "We are told that the distance is 45 km.<BR>\n" );
document.write( "d = 45 km<BR>\n" );
document.write( "We are told the downstream time is 3 hr.<BR>\n" );
document.write( "t = 3 hr<BR>\n" );
document.write( "So,<BR>\n" );
document.write( "45 = r*3<BR>\n" );
document.write( "Dividing both sides by 3:<BR>\n" );
document.write( "15 = r<BR>\n" );
document.write( "r = 15 km/hr.<BR>\n" );
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document.write( "The downstream rate will be the speed of the boat plus the speed of the current:   b+c.<BR>\n" );
document.write( "(b+c) = 15 km/hr<BR>\n" );
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document.write( "We also are told the return time upstream was 5 hr.<BR>\n" );
document.write( "45 = r*5<BR>\n" );
document.write( "Dividing both sides by 5:<BR>\n" );
document.write( "9 = r<BR>\n" );
document.write( "r = 9 km/hr<BR>\n" );
document.write( "The upstream rate will be the speed of the boat minus the speed of the current: b-c.<BR>\n" );
document.write( "(b-c) = 9 km/hr<BR>\n" );
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document.write( "Now we have two linear equations:<BR>\n" );
document.write( "b + c = 15<BR>\n" );
document.write( "b - c =  9<BR>\n" );
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document.write( "Adding them we have:<BR>\n" );
document.write( "2b = 24<BR>\n" );
document.write( "Dividing both sides by 2<BR>\n" );
document.write( "b = 12<BR>\n" );
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document.write( "Substitute b=12  into the downstream equation to find 'c':<BR>\n" );
document.write( "12 + c = 15<BR>\n" );
document.write( "c = 3<BR>\n" );
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document.write( "Check by substituting into the upstream equation:<BR>\n" );
document.write( "12 -3 = 9.  True.<BR>\n" );
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document.write( "So, the rate of the boat in calm water is 12 km/hr, and the rate of the current is 3 km/hr.<BR>\n" );
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document.write( "Done. </SPAN>\n" );
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