document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=830766>Question 830766</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A river is one kilometer wide and flows with a uniform stream velocity. A ship sailing at full speed needs 12 minutes to cover one kilometer upstream, and 3 minutes to cover one kilometer downstream. What is the shortest time in which the ship can cross the river to the nearest point on the opposite bank? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #500920 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=500920\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> ---<BR>\n" );
document.write( "x = ship speed<BR>\n" );
document.write( "y = water speed<BR>\n" );
document.write( "---<BR>\n" );
document.write( "s = d/t<BR>\n" );
document.write( "t = d/s<BR>\n" );
document.write( "---<BR>\n" );
document.write( "up:<BR>\n" );
document.write( "12 = 1/(x - y)<BR>\n" );
document.write( "---<BR>\n" );
document.write( "down:<BR>\n" );
document.write( "3 = 1/(x + y)<BR>\n" );
document.write( "---<BR>\n" );
document.write( "linear system:<BR>\n" );
document.write( "12 = 1/(x - y)<BR>\n" );
document.write( "3 = 1/(x + y)<BR>\n" );
document.write( "---<BR>\n" );
document.write( "put the system of linear equations into standard form:<BR>\n" );
document.write( "---<BR>\n" );
document.write( "12(x - y) = 1<BR>\n" );
document.write( "3(x + y) = 1<BR>\n" );
document.write( "---<BR>\n" );
document.write( "12x - 12y = 1<BR>\n" );
document.write( "3x + 3y = 1<BR>\n" );
document.write( "---<BR>\n" );
document.write( "copy and paste the above linear system in standard form into this matrix-method solver:<BR>\n" );
document.write( "https://sooeet.com/math/system-of-linear-equations-solver.php<BR>\n" );
document.write( "---<BR>\n" );
document.write( "speeds:<BR>\n" );
document.write( "x = ship speed = 0.20833333 km/min<BR>\n" );
document.write( "y = water speed = 0.125 km/min<BR>\n" );
document.write( "---<BR>\n" );
document.write( "perpendicular river crossing, 1-km bank to bank:<BR>\n" );
document.write( "---<BR>\n" );
document.write( "make a right triangle with:<BR>\n" );
document.write( "hypotenuse = ship speed <BR>\n" );
document.write( "side-a = water speed<BR>\n" );
document.write( "side-b = net ship speed<BR>\n" );
document.write( "---<BR>\n" );
document.write( "hh = aa + bb<BR>\n" );
document.write( "bb = hh - aa<BR>\n" );
document.write( "b = sqrt( hh - aa )<BR>\n" );
document.write( "b = sqrt( 0.20833333^2 - 0.125^2 )<BR>\n" );
document.write( "b = 0.16666666 km/min<BR>\n" );
document.write( "---<BR>\n" );
document.write( "s = d/t<BR>\n" );
document.write( "t = d/s<BR>\n" );
document.write( "---<BR>\n" );
document.write( "t = (1 km) / (0.16666666 km/min)<BR>\n" );
document.write( "t = 6.0 min<BR>\n" );
document.write( "---<BR>\n" );
document.write( "answer:<BR>\n" );
document.write( "time required to cross the 1-kilometer wide river to the nearest point on the opposite bank = 6 minutes<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Solve and graph linear equations:<BR>\n" );
document.write( "https://sooeet.com/math/linear-equation-solver.php<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Solve quadratic equations, quadratic formula:<BR>\n" );
document.write( "https://sooeet.com/math/quadratic-formula-solver.php<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Solve systems of linear equations up to 6-equations 6-variables:<BR>\n" );
document.write( "https://sooeet.com/math/system-of-linear-equations-solver.php </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );