document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=212720>Question 212720</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0321269470/algebrahomeworkh>Introductory Algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Please help!! I have tried to come up with a solution...but I am majorly stuck and frustrated!! If I've made an error, I can't see it. And with what I do have, I have no idea what the next step should be. ~ Thanks! Here's the problem and my attempt:\r<BR>\n" );
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document.write( "Boat Speed.     The current in a stream moves at a speed of 3 mph. A boat travels 45 mi upstream and 45 mi downstream in a total time of 8 hr. What is the speed of the boat in still water?\r<BR>\n" );
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document.write( "t(1) = 45/r-3      t(2) = 45/r+3       t(1) + t(2) = 8, where r is the rate of the boat in still water \r<BR>\n" );
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document.write( "45/(r-3)+ 45/(r+3)=8  The LCD is (r-3)(r+3)\r<BR>\n" );
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document.write( "((r-3) (r+3) (45/(r-3)) + ((r-3) (r+3) (45/(r+3)) = 8 (r-3)(r+3) \r<BR>\n" );
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document.write( "45 (r + 3) + 45 (r - 3) = 8 (r^2 – 9)\r<BR>\n" );
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document.write( "45r + 135 + 45r – 135 = 8r^2 – 72\r<BR>\n" );
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document.write( "90r = 8r^2 – 72<BR>\n" );
document.write( "-90r        -90r\r<BR>\n" );
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document.write( "0 = 8r2 – 90r – 72\r<BR>\n" );
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document.write( "Now What? I know the next step is to factor but I can’t determine a factorization in the form of (x + ?)(x - ?)…the best I can do is…\r<BR>\n" );
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document.write( "0 = 2 (r^2 – 45r – 32)\r<BR>\n" );
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document.write( "And IF this is the correct factoring answer…I have NO CLUE what to do next! PLEASE HELP!!<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #160638 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=160638\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Boat Speed. The current in a stream moves at a speed of 3 mph. A boat travels 45 mi upstream and 45 mi downstream in a total time of 8 hr. What is the speed of the boat in still water?<BR>\n" );
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document.write( "Applying the distance formula:<BR>\n" );
document.write( "d = rt)<BR>\n" );
document.write( "Solving for t:<BR>\n" );
document.write( "t = d/r<BR>\n" );
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document.write( "Let r = speed of boat in still water<BR>\n" );
document.write( "then<BR>\n" );
document.write( "\"time going upstream\" + \"time going downstream\" = 8<BR>\n" );
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document.write( "45/(r-3) + 45/(r+3) = 8<BR>\n" );
document.write( "Now, multiplying both sides by (r-3)(r+3):<BR>\n" );
document.write( "45(r+3) + 45(r-3) = 8(r-3)(r+3)<BR>\n" );
document.write( "Expanding:<BR>\n" );
document.write( "45r+135 + 45r-135 = 8(r^2-9)<BR>\n" );
document.write( "45r+45r = 8r^2-72<BR>\n" );
document.write( "90r = 8r^2-72<BR>\n" );
document.write( "0 = 8r^2-90r-72  (Exactly what you had)<BR>\n" );
document.write( "Solving for r using the quadratic formula yields:<BR>\n" );
document.write( "r = {12, -0.75}<BR>\n" );
document.write( "We can toss out the negative answer leaving:<BR>\n" );
document.write( "r = 12 mph<BR>\n" );
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document.write( "Details of quadratic to follow:<BR>\n" );
document.write( "<TABLE  BORDER=1>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=quadratic.solver>SOLVE quadratic equation with variable</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ar%5E2%2Bbr%2Bc=0 ALIGN=MIDDLE  ALT=\"ar%5E2%2Bbr%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8r%5E2%2B-90r%2B-72+=+0 ALIGN=MIDDLE  ALT=\"8r%5E2%2B-90r%2B-72+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"r%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For these solutions to exist, the <U>discriminant</U> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be a negative number.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  First, we need to compute the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%28-90%29%5E2-4%2A8%2A-72=10404 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-90%29%5E2-4%2A8%2A-72=10404\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=10404 is greater than zero. That means that there are two solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B12%5D+=+%28--90%2B-sqrt%28+10404+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--90%2B-sqrt%28+10404+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5B1%5D+=+%28-%28-90%29%2Bsqrt%28+10404+%29%29%2F2%5C8+=+12 ALIGN=MIDDLE  ALT=\"r%5B1%5D+=+%28-%28-90%29%2Bsqrt%28+10404+%29%29%2F2%5C8+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5B2%5D+=+%28-%28-90%29-sqrt%28+10404+%29%29%2F2%5C8+=+-0.75 ALIGN=MIDDLE  ALT=\"r%5B2%5D+=+%28-%28-90%29-sqrt%28+10404+%29%29%2F2%5C8+=+-0.75\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <BR>\n" );
document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8r%5E2%2B-90r%2B-72 ALIGN=MIDDLE  ALT=\"8r%5E2%2B-90r%2B-72\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be factored:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8r%5E2%2B-90r%2B-72+=+8%28r-12%29%2A%28r--0.75%29 ALIGN=MIDDLE  ALT=\"8r%5E2%2B-90r%2B-72+=+8%28r-12%29%2A%28r--0.75%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 12, -0.75.\n" );
document.write( "Here's your graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+8%2Ax%5E2%2B-90%2Ax%2B-72+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+8%2Ax%5E2%2B-90%2Ax%2B-72+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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