document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=919232>Question 919232</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello! I could use some help with this word problem. \r<BR>\n" );
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document.write( "To celebrate Lewis and Clark expedition, you are traveling 40 miles upstream and then 40 miles downstream in a canoe. The speed of the river current is 5 miles an hour. If the trip takes you 5 hours, how fast do you travel if the river has no current? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #557590 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=557590\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let b = speed of boat in mph\r<BR>\n" );
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document.write( "Upstream: You go slower since you are going against the current. The actual speed is b-5. The \"-5\" is due to the 5 mph current slowing you down.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40+=+%28b-5%29%2At ALIGN=MIDDLE  ALT=\"40+=+%28b-5%29%2At\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40%2F%28b-5%29+=+t ALIGN=MIDDLE  ALT=\"40%2F%28b-5%29+=+t\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+40%2F%28b-5%29 ALIGN=MIDDLE  ALT=\"t+=+40%2F%28b-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "It takes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40%2F%28b-5%29 ALIGN=MIDDLE  ALT=\"40%2F%28b-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > hours to go upstream\r<BR>\n" );
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document.write( "-------------------------------------------------------\r<BR>\n" );
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document.write( "Upstream: You go faster since you are going with the current. The actual speed is b+5. The \"+5\" is due to the 5 mph current speeding you up.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D+=+r%2At ALIGN=MIDDLE  ALT=\"D+=+r%2At\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40+=+%28b%2B5%29%2At ALIGN=MIDDLE  ALT=\"40+=+%28b%2B5%29%2At\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40%2F%28b%2B5%29+=+t ALIGN=MIDDLE  ALT=\"40%2F%28b%2B5%29+=+t\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+40%2F%28b%2B5%29 ALIGN=MIDDLE  ALT=\"t+=+40%2F%28b%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "It takes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40%2F%28b%2B5%29 ALIGN=MIDDLE  ALT=\"40%2F%28b%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > hours to go downstream\r<BR>\n" );
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document.write( "-------------------------------------------------------\r<BR>\n" );
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document.write( "Add up the two time expressions <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40%2F%28b-5%29 ALIGN=MIDDLE  ALT=\"40%2F%28b-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40%2F%28b%2B5%29 ALIGN=MIDDLE  ALT=\"40%2F%28b%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40%2F%28b-5%29+%2B+40%2F%28b%2B5%29 ALIGN=MIDDLE  ALT=\"40%2F%28b-5%29+%2B+40%2F%28b%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Set this sum equal to 5 because the two time values must add to 5 hours. This is the total round trip time.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40%2F%28b-5%29+%2B+40%2F%28b%2B5%29+=+5 ALIGN=MIDDLE  ALT=\"40%2F%28b-5%29+%2B+40%2F%28b%2B5%29+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now we solve for b.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40%28b%2B5%29+%2B+40%28b-5%29+=+5%28b-5%29%28b%2B5%29 ALIGN=MIDDLE  ALT=\"40%28b%2B5%29+%2B+40%28b-5%29+=+5%28b-5%29%28b%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by the LCD <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28b-5%29%28b%2B5%29 ALIGN=MIDDLE  ALT=\"%28b-5%29%28b%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to clear out the fractions.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40%28b%2B5%29+%2B+40%28b-5%29+=+5%28b%5E2-25%29 ALIGN=MIDDLE  ALT=\"40%28b%2B5%29+%2B+40%28b-5%29+=+5%28b%5E2-25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40b%2B200+%2B+40b-200+=+5b%5E2-125 ALIGN=MIDDLE  ALT=\"40b%2B200+%2B+40b-200+=+5b%5E2-125\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=80b+=+5b%5E2-125 ALIGN=MIDDLE  ALT=\"80b+=+5b%5E2-125\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+5b%5E2-125-80b ALIGN=MIDDLE  ALT=\"0+=+5b%5E2-125-80b\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5b%5E2-80b-125+=+0 ALIGN=MIDDLE  ALT=\"5b%5E2-80b-125+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%28b%5E2-16b-25%29+=+0 ALIGN=MIDDLE  ALT=\"5%28b%5E2-16b-25%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-16b-25+=+0 ALIGN=MIDDLE  ALT=\"b%5E2-16b-25+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Use the quadratic formula to get these solutions:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=8%2Bsqrt%2889%29 ALIGN=MIDDLE  ALT=\"b=8%2Bsqrt%2889%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=8-sqrt%2889%29 ALIGN=MIDDLE  ALT=\"b=8-sqrt%2889%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The solutions approximate to\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=17.4339811320567 ALIGN=MIDDLE  ALT=\"b=17.4339811320567\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+-1.4339811320566 ALIGN=MIDDLE  ALT=\"b+=+-1.4339811320566\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Toss out the negative answer because a negative speed makes no sense in this case.\r<BR>\n" );
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document.write( "The exact answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=8%2Bsqrt%2889%29 ALIGN=MIDDLE  ALT=\"b=8%2Bsqrt%2889%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. The approximate answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=17.4339811320567 ALIGN=MIDDLE  ALT=\"b=17.4339811320567\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Let me know if you need more help or if you need me to explain a step in more detail.<BR>\n" );
document.write( "Feel free to email me at <a  rel=nofollow HREF=\"mailto:jim_thompson5910@hotmail.com?Subject=I%20Need%20Algebra%20Help\">jim_thompson5910@hotmail.com</a><BR>\n" );
document.write( "or you can visit my website here: <a  rel=nofollow HREF=\"http://www.freewebs.com/jimthompson5910/home.html\">http://www.freewebs.com/jimthompson5910/home.html</a>\r<BR>\n" );
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document.write( "Thanks,\r<BR>\n" );
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document.write( "Jim  </SPAN>\n" );
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