document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=64946>Question 64946</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A boy started on a trip across a lake by a motorboat. After he had travelled 15 km, the motor failed and he had to use a banca for the remaining 6 km to his destination. His average speed by motor was 4 kph  faster than his average speed while rowing a banca. If the entire trip took five and a half hours, what was his average speed while rowing ?\r<BR>\n" );
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document.write( "dear tuitor , <BR>\n" );
document.write( "    ihave been trying this problem too many times but cant. This what i get\r<BR>\n" );
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document.write( "d = rt<BR>\n" );
document.write( "motorboat  d= 15 km     r= r+4    t = t<BR>\n" );
document.write( "banca      d= 6 km      r= r      t= 5.5 - t </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #45413 by </B><A HREF=/tutors/aboutme.mpl?userid=ptaylor><B>ptaylor(2198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ptaylor><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=ptaylor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=45413\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You have definitely got the right formula so that's a big plus. The way I worked it, we end up with a quadratic equation which makes it a little more complicated than most word problems. Maybe another tutor will find an easier way. \r<BR>\n" );
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document.write( "As you suggest, we'll use the formula: d=rt or t=d/r\r<BR>\n" );
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document.write( "Let r=average speed in banca<BR>\n" );
document.write( "Average speed by motor, we are told, is r+4\r<BR>\n" );
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document.write( "Now we know that the time spent in the banca (6/r) plus the time spent in the motorboat (15/(r+4)) equals 5.5 hours so our equation to solve is:\r<BR>\n" );
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document.write( "(6/r)+15/(r+4)=5.5  multiply both sides by(r)(r+4) to get rid of the fractions and r's in the denominator:\r<BR>\n" );
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document.write( "((r)(r+4))(6/r)+(15(r)(r+4))/(r+4)=5.5(r)(r+4) simplifying we get:\r<BR>\n" );
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document.write( "6(r+4)+15r=5.5r^2+22r  further simplifying:<BR>\n" );
document.write( "6r+24+15r=5.5r^2+22r   which gives:<BR>\n" );
document.write( "5.5r^2+22r-21r-24=0<BR>\n" );
document.write( "5.5r^2+r-24=0  Now we'll solve this using the quadratic formula:\r<BR>\n" );
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document.write( "r=(-1+or-sqrt(1+528))/11<BR>\n" );
document.write( "r=(-1+or-(23))/11\r<BR>\n" );
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document.write( "r=+22/11 or<BR>\n" );
document.write( "r=2mph rowing speed\r<BR>\n" );
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document.write( "r also has a negative value which we will discount<BR>\n" );
document.write( "r+4=2+4= 6mph speed of the boat\r<BR>\n" );
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document.write( "ck<BR>\n" );
document.write( "6/2+15/6=5.5<BR>\n" );
document.write( "3+2.5=5.5<BR>\n" );
document.write( "5.5=5.5\r<BR>\n" );
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document.write( "Hope this helps.  Happy holidays-----ptaylor\r<BR>\n" );
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document.write( " </SPAN>\n" );
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