document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=40450>Question 40450</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A man gets in his motorboat and travels upstream. 1 mile up the river, his hat flys off, but he doesn't notice for another 5 minutes. When he finally does notice, he immediately goes back in persuit of it. He finally catches up to it floating by his starting point. Assuming that the boat was traveling the same speed the whole time, how fast was the river flowing? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #25916 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=25916\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> b = rate of boat<BR>\n" );
document.write( "r = rate of river<BR>\n" );
document.write( "There are 2 combined distances that the boat travels. Ther is the 1 mile<BR>\n" );
document.write( "distance and the distance beyond 1 mile which takes the boat 5 minutes<BR>\n" );
document.write( "going against the current.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%281%29+=+1 ALIGN=MIDDLE  ALT=\"d%281%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%282%29+=+%28b+-+r%29%2A5 ALIGN=MIDDLE  ALT=\"d%282%29+=+%28b+-+r%29%2A5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "b - r is the boats rate going upstream<BR>\n" );
document.write( "(b - r)*5 is rate x time  = distance<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%281%29+%2B+d%282%29 ALIGN=MIDDLE  ALT=\"d%281%29+%2B+d%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the combined distance<BR>\n" );
document.write( "When the boater goes back to get the hat, he will go back to his starting <BR>\n" );
document.write( "point at a rate of (b + r) going with the current. His time is the <BR>\n" );
document.write( "combined distances divided by his rate.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%281+%2B+%28b+-+r%29%2A5%29+%2F+%28b+%2B+r%29 ALIGN=MIDDLE  ALT=\"t+=+%281+%2B+%28b+-+r%29%2A5%29+%2F+%28b+%2B+r%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "During this time, the hat floats downstream for 1 mile back to the <BR>\n" );
document.write( "starting point at the rate the river is flowing.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+1+%2F+r ALIGN=MIDDLE  ALT=\"t+=+1+%2F+r\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "These times are equal so,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%281+%2B+%28b+-+r%29%2A5%29+%2F+%28b+%2B+r%29+=+1+%2F+r ALIGN=MIDDLE  ALT=\"t+=+%281+%2B+%28b+-+r%29%2A5%29+%2F+%28b+%2B+r%29+=+1+%2F+r\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+%2B+r%28b+-+r%29%2A5+=+b+%2B+r ALIGN=MIDDLE  ALT=\"r+%2B+r%28b+-+r%29%2A5+=+b+%2B+r\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+%2B+%28br+-+r%5E2%29%2A5+=+b+%2B+r ALIGN=MIDDLE  ALT=\"r+%2B+%28br+-+r%5E2%29%2A5+=+b+%2B+r\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5r%5E2+%2B+5br+-+b+=+0 ALIGN=MIDDLE  ALT=\"-5r%5E2+%2B+5br+-+b+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5r%5E2+-5br+%2Bb+=+0 ALIGN=MIDDLE  ALT=\"5r%5E2+-5br+%2Bb+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E2+-+br+%2B+b%2F5+=+0 ALIGN=MIDDLE  ALT=\"r%5E2+-+br+%2B+b%2F5+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "complete the square<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E2+-+br+%2B+%28b%5E2%29%2F4+=+%28b%5E2%29%2F4+-+b%2F5 ALIGN=MIDDLE  ALT=\"r%5E2+-+br+%2B+%28b%5E2%29%2F4+=+%28b%5E2%29%2F4+-+b%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28r+-+b%2F2%29%5E2+=+%28b%5E2%29%2F4+-+b%2F5 ALIGN=MIDDLE  ALT=\"%28r+-+b%2F2%29%5E2+=+%28b%5E2%29%2F4+-+b%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+-+b%2F2+=+0%2B-sqrt%28%28%28b%5E2%29%2F4%29+-+b%2F5%29 ALIGN=MIDDLE  ALT=\"r+-+b%2F2+=+0%2B-sqrt%28%28%28b%5E2%29%2F4%29+-+b%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+b%2F2+%2B-sqrt%28%28%28b%5E2%29%2F4%29+-+b%2F5%29 ALIGN=MIDDLE  ALT=\"r+=+b%2F2+%2B-sqrt%28%28%28b%5E2%29%2F4%29+-+b%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Try different values for b, speed of boat to get values for r </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );