document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=157391>Question 157391</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A cruise boat travels 48 miles downstream in 3 hours and returns upstream in 6 hours. Find the rate of the stream. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #116006 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=116006\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let B = rate or boat.<BR>\n" );
document.write( "let S = rate of stream.<BR>\n" );
document.write( "rate * time = distance.<BR>\n" );
document.write( "going downstream, the rate of travel is the rate of the boat plus the rate of the stream.<BR>\n" );
document.write( "going upstream, the rate of travel is the rate of the boat minus the rate of the stream.<BR>\n" );
document.write( "in equation form, this becomes.<BR>\n" );
document.write( "(B+S)*3=48 (going downstream)<BR>\n" );
document.write( "(B-S)*6=48 (going upstream)<BR>\n" );
document.write( "since the distance is the same both times, these equations are equal to each other.<BR>\n" );
document.write( "(B+S)*3=(B-S)*6<BR>\n" );
document.write( "multiplying out.<BR>\n" );
document.write( "becomes 3*B+3*S=6*B-6*S<BR>\n" );
document.write( "becomes 9*S=3*B<BR>\n" );
document.write( "becomes B=3*S<BR>\n" );
document.write( "in the going downstream equation, 3*B+3*S = 48.<BR>\n" );
document.write( "substituting 3*S for B, the equation becomes 3*(3*S) + 3*S = 48<BR>\n" );
document.write( "which becomes 9*S + 3*S = 48<BR>\n" );
document.write( "which becomes 12*S = 48<BR>\n" );
document.write( "which becomes S = 4.<BR>\n" );
document.write( "if S = 4, then the going downstream equation of 3*B + 3*S = 48<BR>\n" );
document.write( "becomes 3*B + 12 = 48<BR>\n" );
document.write( "becomes 3*B = 36<BR>\n" );
document.write( "becomes B = 12.<BR>\n" );
document.write( "the rate of the stream is 4 miles per hour and the rate of the boat is 12 miles per hour.<BR>\n" );
document.write( "going downstream, the combined rate is 16 miles per hour.<BR>\n" );
document.write( "48 miles / 16 yields 3 hours so math is confirmed for the downstream equation.<BR>\n" );
document.write( "going upstream, the combined rate is 8 miles per hour.<BR>\n" );
document.write( "48 miles / 8 yields 6 hours so math is confirmed for the upstream equation.<BR>\n" );
document.write( "answer is the stream is traveling at 4 miles per hour downstream.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "becomes  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );