document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=870229>Question 870229</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A river flows with a uniform velocity v. A person in a motorboat travels 1000m upstream, at which time a log is seen floating by. The person continues to travel upstream for 60.0min at the same speed and then returns downstream to the starting point, where the same log is seen again. Find the velocity of the river.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #524737 by </B><A HREF=/tutors/aboutme.mpl?userid=mananth><B>mananth(16946)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mananth><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=mananth><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=524737\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A river flows with a uniform velocity v. A person in a motorboat travels 1000m upstream, at which time a log is seen floating by. The person continues to travel upstream for 60.0min at the same speed and then returns downstream to the starting point, where the same log is seen again. Find the velocity of the river. \r<BR>\n" );
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document.write( "speed of current = v\r<BR>\n" );
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document.write( "distance traveled = 1000 m\r<BR>\n" );
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document.write( "time = 1 hour<BR>\n" );
document.write( "boat speed = 1000m/hr\r<BR>\n" );
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document.write( "upstream speed = (1000-v)<BR>\n" );
document.write( "distance traveled = 1000 m<BR>\n" );
document.write( "t= 1000/(1000-v)\r<BR>\n" );
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document.write( "down stream speed = (1000+v)<BR>\n" );
document.write( "distance = 2000 m\r<BR>\n" );
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document.write( "t= 2000/(1000+v)\r<BR>\n" );
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document.write( "total time to reach starting point = 1000/(1000-v)+ 2000/(1000+v)\r<BR>\n" );
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document.write( "Now the speed of log = v<BR>\n" );
document.write( "distance = 1000 m<BR>\n" );
document.write( "t= 1000/v\r<BR>\n" );
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document.write( "1000/v = 1000/(1000-v)+ 2000/(1000+v)\r<BR>\n" );
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document.write( "1000(1000^2-v^2)=1000v(1000+v)+2000v(1000-v)\r<BR>\n" );
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document.write( "10^9 -1000v^2=10^6v+1000v^2+2*10^6v-2000v^2\r<BR>\n" );
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document.write( "3*10^6v=10^9\r<BR>\n" );
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document.write( "v=10^9/3*10^6\r<BR>\n" );
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document.write( "100/3\r<BR>\n" );
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document.write( "333.33 mts/h\r<BR>\n" );
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document.write( "CHECK\r<BR>\n" );
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document.write( "Time for log to reach starting point<BR>\n" );
document.write( "t=d/r<BR>\n" );
document.write( "=1000/333=3.005 hour\r<BR>\n" );
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document.write( "Time for boat to go upstream <BR>\n" );
document.write( "=1000/(1000-v)<BR>\n" );
document.write( "=1000/667<BR>\n" );
document.write( "=1.5 hours<BR>\n" );
document.write( "time for boat to starting point <BR>\n" );
document.write( "2000/(1000+v)<BR>\n" );
document.write( "=2000/1333<BR>\n" );
document.write( "=1.5 hours\r<BR>\n" );
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document.write( "boat time upstream + time downstream = 3 hours<BR>\n" );
document.write( "Time for log to reach starting point =3.005 hours<BR>\n" );
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