document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=808958>Question 808958</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the current in a stream moves at a speed of 9 mph. a boat travels 4 mi upstream and 4 mi downstream in a total of 4 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 #487316 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39616)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=487316\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> ASSIGN VARIABLES<BR>\n" );
document.write( "r = boat speed when no current present<BR>\n" );
document.write( "c = current speed<BR>\n" );
document.write( "d = travel distance in either direction, up or down stream<BR>\n" );
document.write( "h = time for round trip up and down stream for the d distance\r<BR>\n" );
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document.write( "QUESTION<BR>\n" );
document.write( "Solve for r.\r<BR>\n" );
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document.write( "A data table may be very helpful.\r<BR>\n" );
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document.write( "DIRECTION___________Speed____________time(hour)___________Distance(miles)<BR>\n" );
document.write( "Upstream____________r-c______________(___)________________d<BR>\n" );
document.write( "Downstream__________r+c______________(___)________________d\r<BR>\n" );
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document.write( "Fill-in the time information.<BR>\n" );
document.write( "DIRECTION___________Speed____________time(hour)___________Distance(miles)<BR>\n" );
document.write( "Upstream____________r-c______________(d/(r-c))________________d<BR>\n" );
document.write( "Downstream__________r+c______________(d/(r+c))________________d<BR>\n" );
document.write( "Total_________________________________h\r<BR>\n" );
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document.write( "The data allows enough information to form a time sum equation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28d%2F%28r-c%29%2Bd%2F%28r%2Bc%29=h%29 ALIGN=MIDDLE  ALT=\"highlight%28d%2F%28r-c%29%2Bd%2F%28r%2Bc%29=h%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Solution Steps:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28d%2F%28r-c%29%29%28r%2Bc%29%28r-c%29%2B%28d%2F%28r%2Bc%29%29%28r%2Bc%29%28r-c%29=h%28r%2Bc%29%28r-c%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >  which is multiply b.s. by LCD<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%28r%2Bc%29%2Bd%28r-c%29=h%28r%5E2-c%5E2%29 ALIGN=MIDDLE  ALT=\"d%28r%2Bc%29%2Bd%28r-c%29=h%28r%5E2-c%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, simplification and recognize difference of two squares<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dr%2Bdc%2Bdr-dc=hr%5E2-hc%5E2 ALIGN=MIDDLE  ALT=\"dr%2Bdc%2Bdr-dc=hr%5E2-hc%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2dr=hr%5E2-hc%5E2 ALIGN=MIDDLE  ALT=\"2dr=hr%5E2-hc%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28hr%5E2-2dr-hc%5E2=0%29 ALIGN=MIDDLE  ALT=\"highlight%28hr%5E2-2dr-hc%5E2=0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > An important chief equation for our solution, entirely in symbolism.\r<BR>\n" );
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document.write( "You would want to solve that quadratic equation for r.  <BR>\n" );
document.write( "The values given in the description may be picked so that the highlighted quadratic equation may be factorable, but we never know ahead of time, unless we are specifically told so.  In this solution, factorability is not assumed.\r<BR>\n" );
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document.write( "Directly using solution to quadratic formula, <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=%282d%2Bsqrt%28%282d%29%5E2-4%2Ah%2A%28-hc%5E2%29%29%29%2F%282%2A2d%29 ALIGN=MIDDLE  ALT=\"r=%282d%2Bsqrt%28%282d%29%5E2-4%2Ah%2A%28-hc%5E2%29%29%29%2F%282%2A2d%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=%282d%2Bsqrt%284d%5E2%2B4%28hc%29%5E2%29%29%2F%284d%29 ALIGN=MIDDLE  ALT=\"r=%282d%2Bsqrt%284d%5E2%2B4%28hc%29%5E2%29%29%2F%284d%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=%282d%2B2%2Asqrt%28d%5E2%2B%28hc%29%5E2%29%29%2F%284d%29 ALIGN=MIDDLE  ALT=\"r=%282d%2B2%2Asqrt%28d%5E2%2B%28hc%29%5E2%29%29%2F%284d%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28r=%28d%2Bsqrt%28d%5E2%2B%28hc%29%5E2%29%29%2F%282d%29%29 ALIGN=MIDDLE  ALT=\"highlight%28r=%28d%2Bsqrt%28d%5E2%2B%28hc%29%5E2%29%29%2F%282d%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >------The answer purely in symbolic form.\r<BR>\n" );
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document.write( "Just substitute the given values from the description and compute r.\r<BR>\n" );
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document.write( "So how about the quadratic equation found?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4r%5E2-2%2A4r-4%2A9%5E2=0 ALIGN=MIDDLE  ALT=\"4r%5E2-2%2A4r-4%2A9%5E2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > when the values are substituted.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E2-2r-81=0 ALIGN=MIDDLE  ALT=\"r%5E2-2r-81=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "While not being factorable, using this form for the general solution of a quadratic formula might be much easier than using purely symbolic form, but again, we never know this ahead of time.  The advantage of doing all work in symbolic form is that if values are different but the basic form of the problem is the same, then you do not need to resolve the same problem again, because it would been already solved symbolically. </SPAN>\n" );
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