document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=139175>Question 139175</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me translate this into a quadratic equation and solve. \r<BR>\n" );
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document.write( "The Hudson River flows at a rate of 3 miles per hour.  A patrol boat travels 60 miles upriver, and returns in a total time of 9 hours.  What is the speed of the boat in still water? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #101548 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=101548\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> he Hudson River flows at a rate of 3 miles per hour. A patrol boat travels 60 miles upriver, and returns in a total time of 9 hours. What is the speed of the boat in still water?<BR>\n" );
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document.write( "Let s = speed of the boat in still water<BR>\n" );
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document.write( "(s-3) = speed upstream<BR>\n" );
document.write( "(s+3) = speed downstream<BR>\n" );
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document.write( "Write a time equation; Time = dist/speed<BR>\n" );
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document.write( "Time upstream + time downstream = 9 hr<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60%2F%28%28s-3%29%29 ALIGN=MIDDLE  ALT=\"60%2F%28%28s-3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60%2F%28%28s%2B3%29%29 ALIGN=MIDDLE  ALT=\"60%2F%28%28s%2B3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 9<BR>\n" );
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document.write( "multiply equation by (s-3)(s+3) to get rid of the denominators:<BR>\n" );
document.write( "(s-3)(s+3)*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60%2F%28%28s-3%29%29 ALIGN=MIDDLE  ALT=\"60%2F%28%28s-3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + (s-3)(s+3)*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60%2F%28%28s%2B3%29%29 ALIGN=MIDDLE  ALT=\"60%2F%28%28s%2B3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 9(s-3)(s+3)<BR>\n" );
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document.write( "60(s+3) + 60(s-3) = 9(s^2 - 9)<BR>\n" );
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document.write( "60s + 180 + 60s - 180 = 9s^2 - 81<BR>\n" );
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document.write( "120s = 9s^2 - 81<BR>\n" );
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document.write( "0 = 9s^2 - 120s - 81<BR>\n" );
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document.write( "Simplify, divide equation by 3, giving us a simple quadratic equation<BR>\n" );
document.write( "3s^2 - 40s - 27 = 0<BR>\n" );
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document.write( "We need to use the quadratic formula to solve for s: a=3; b=-40; c=-27<BR>\n" );
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document.write( "The positive solution = 13.977 ~ 14 mph<BR>\n" );
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document.write( "Check solution using 14 mph<BR>\n" );
document.write( "60/17 + 60/11 =<BR>\n" );
document.write( "3.529 + 5.454 = 8.983 ~ 9 hrs </SPAN>\n" );
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