document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1207221>Question 1207221</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A motorboat travels the distance from one pier to another pier in 4 hours and the way back in 5 hours. What is the speed of the boat in still water if it travels 70 km with the current in 3.5 hours? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #844968 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13203)</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=844968\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "I will leave it to other tutors to provide some form of a formal algebraic solution to the problem.<br><BR>\n" );
document.write( "I will show a much faster and less formal solution that uses logical reasoning and simple mental arithmetic.<br><BR>\n" );
document.write( "Obviously, the shorter 4-hour trip is with the current and the longer 5-hour trip is against the current.<br><BR>\n" );
document.write( "The boat can travel 70km with the current in 3.5 hours.<br><BR>\n" );
document.write( "Use that to determine that the speed of the boat with the current is 70/3.5 = 20km/h; then use that to determine that the distance of the trip is 4*20=80km.<br><BR>\n" );
document.write( "Alternatively, you can do that calculation using a proportion that says the distance is proportional to the speed: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F70=4%2F3.5 ALIGN=MIDDLE  ALT=\"x%2F70=4%2F3.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<br><BR>\n" );
document.write( "The trip is the same distance each direction.  Since the ratio of times is 5:4, the ratio of speeds (with and against the current) is 4:5.  So the speed against the current is 4/5 of the speed with the current: (4/5)(20) = 16km/h.<br><BR>\n" );
document.write( "So the speed with the current is 20km/h and the speed against the current is 16km/h.  Although it is a simple algebra problem to determine the speed of the current and the speed of the boat, logical reasoning tells us that the speed of the boat is halfway between 16km/h and 20km/h, or 18km/h, and the speed of the current is the difference between 18km/h and either 16km/h or 20km/h.<br><BR>\n" );
document.write( "ANSWER: The speed of the boat in still water is 18km/h (and the speed of the current is 2km/h)<br><BR>\n" );
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