document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=934432>Question 934432</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A BOAT CAPABLE OF MOVING IN STILL WATER WITH A SPEED OF 10 KM/HR CROSSES A RIVER 2 KM BROAD FLOWING WITH A SPEED OF 6 KM/HR. FIND THE TIME OF CROSSING BY THE SHORTEST ROUTE, AND FIND THE MINIMUM TIME OF CROSSING </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #567427 by </B><A HREF=/tutors/aboutme.mpl?userid=TimothyLamb><B>TimothyLamb(4379)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=TimothyLamb><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=TimothyLamb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=567427\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> first, the shortest route is directly across the 2 km width ...<BR>\n" );
document.write( "to cross this way the boat must aim into the current at an angle to negate the speed of the current:<BR>\n" );
document.write( "---<BR>\n" );
document.write( "set up a right triangle with:<BR>\n" );
document.write( "h = hypotenuse = boat speed in still water = 10 kph<BR>\n" );
document.write( "a = short leg = current speed = 6 kph<BR>\n" );
document.write( "x = long leg = effective speed of boat in the current<BR>\n" );
document.write( "---<BR>\n" );
document.write( "h = sqrt( aa + xx )<BR>\n" );
document.write( "10 = sqrt( 6*6 + xx )<BR>\n" );
document.write( "( 10 = sqrt( 6*6 + xx ) )^2<BR>\n" );
document.write( "10*10 = 6*6 + xx<BR>\n" );
document.write( "xx = 10*10 - 6*6<BR>\n" );
document.write( "x = sqrt( 10*10 - 6*6 )<BR>\n" );
document.write( "x = 8 kph<BR>\n" );
document.write( "---<BR>\n" );
document.write( "s = d/t<BR>\n" );
document.write( "t = d/s<BR>\n" );
document.write( "t = 2/8<BR>\n" );
document.write( "t = 0.25 hours = 15 minutes<BR>\n" );
document.write( "---<BR>\n" );
document.write( "answer A:<BR>\n" );
document.write( "time to cross by the shortest distance route = 15 minutes<BR>\n" );
document.write( "---<BR>\n" );
document.write( "now, the minimum crossing time ...<BR>\n" );
document.write( "the fastest crossing is when the boat aims directly perpendicular to the current:<BR>\n" );
document.write( "---<BR>\n" );
document.write( "set up a right triangle with:<BR>\n" );
document.write( "h = hypotenuse = effective speed of boat in the current<BR>\n" );
document.write( "a = short leg = current speed = 6 kph<BR>\n" );
document.write( "x = long leg = boat speed in still water = 10 kph<BR>\n" );
document.write( "---<BR>\n" );
document.write( "to calculate this crossing time we only need to know x, the speed of the boat perpendicular to the current, which we know is 10 kph:<BR>\n" );
document.write( "---<BR>\n" );
document.write( "t = d/s<BR>\n" );
document.write( "t = 2/10<BR>\n" );
document.write( "t = 0.20 hours = 12 minutes<BR>\n" );
document.write( "---<BR>\n" );
document.write( "answer B:<BR>\n" );
document.write( "the minimum crossing time = 12 minutes<BR>\n" );
document.write( "---<BR>\n" );
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document.write( "</TD></TR></TABLE>\n" );