document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=733604>Question 733604</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a boatman goes 96 km in 8 hours with the flow of a river and returns in 12 hours (against the flow). what Will be the respective speed of the boat and the river (in km/hour)? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #852788 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13258)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=852788\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br>\r<BR>\n" );
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document.write( "The response from the other tutor shows a typical formal algebraic solution -- which the student certainly should understand.<br><BR>\n" );
document.write( "There are occasions where a quick mental solution is advantageous -- as in a timed competitive exam.<br><BR>\n" );
document.write( "Furthermore, solving the problem informally is good brain exercise.<br><BR>\n" );
document.write( "Going with the current, the boat goes 96 km in 8 hours, so its speed with the current is 96/8 = 12 km/hr.<BR>\n" );
document.write( "Going against the current, the boat goes 96 km in 12 hours, so its speed against the current is 96/12 = 8 km/hr.<br><BR>\n" );
document.write( "So ADDing the speed of the current to the speed of the boat gives a speed of 12 km/hr, while SUBTRACTing the speed of the current from the speed of the boat gives a speed of 8 km/hr.<br><BR>\n" );
document.write( "Logical reasoning then tells us that the speed of the boat is halfway between those two speeds, which is 10 km/hr; and that makes the speed of the current 2 km/hr.<br><BR>\n" );
document.write( "ANSWERS: boat speed 10 km/hr; current speed 2 km/hr<br><BR>\n" );
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