document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=172638>Question 172638</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0321233832/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Ineed your help once again I try own my own and my answer are looking craazt help is needed.  Thank you so much\r<BR>\n" );
document.write( "\n" );
document.write( "Steve traveled 200 miles at a certain speed. Had he gone 10mph faster, the trip would have taken 1 hour less. Find the speed of his vehicle\r<BR>\n" );
document.write( "\n" );
document.write( "can you show me this one too.\r<BR>\n" );
document.write( "\n" );
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?\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #127498 by </B><A HREF=/tutors/aboutme.mpl?userid=Mathtut><B>Mathtut(3670)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Mathtut><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=127498\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I set up the equations you solve<BR>\n" );
document.write( ":<BR>\n" );
document.write( "d=rt........in both instances distance is equal<BR>\n" );
document.write( "lets call the rate of the slow trip r and time t<BR>\n" );
document.write( "lets call the rate of the fast trip r+10 and time(t-1)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "so 200=rt...eq 1<BR>\n" );
document.write( "...200=(r+10)(t-1)..eq 2<BR>\n" );
document.write( ":change eq 1 to t=200/r and substitute it into eq 2 and solve for r...this will involves a quadratic equation again<BR>\n" );
document.write( ":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200=%28r%2B10%29%28%28200%2Fr%29-1%29 ALIGN=MIDDLE  ALT=\"200=%28r%2B10%29%28%28200%2Fr%29-1%29\"   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=200=%28r%2B10%29%28%28200-r%29%2Fr%29 ALIGN=MIDDLE  ALT=\"200=%28r%2B10%29%28%28200-r%29%2Fr%29\"   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=200r=%28r%2B10%29%28200-r%29 ALIGN=MIDDLE  ALT=\"200r=%28r%2B10%29%28200-r%29\"   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=200r=200r-r%5E2%2B2000-10r ALIGN=MIDDLE  ALT=\"200r=200r-r%5E2%2B2000-10r\"   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%5E2%2B10r-2000=0 ALIGN=MIDDLE  ALT=\"r%5E2%2B10r-2000=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "throw out negative value<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28r=40%2Cr=-50%29 ALIGN=MIDDLE  ALT=\"system%28r=40%2Cr=-50%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28r=40%29 ALIGN=MIDDLE  ALT=\"highlight%28r=40%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >mph and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28r%2B10%29 ALIGN=MIDDLE  ALT=\"highlight%28r%2B10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=50mph<BR>\n" );
document.write( ":\r<BR>\n" );
document.write( "\n" );
document.write( " <TABLE  BORDER=1>\n" );
document.write( "\n" );
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=1r%5E2%2B10r%2B-2000+=+0 ALIGN=MIDDLE  ALT=\"1r%5E2%2B10r%2B-2000+=+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=%2810%29%5E2-4%2A1%2A-2000=8100 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2810%29%5E2-4%2A1%2A-2000=8100\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=8100 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+=+%28-10%2B-sqrt%28+8100+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-10%2B-sqrt%28+8100+%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-%2810%29%2Bsqrt%28+8100+%29%29%2F2%5C1+=+40 ALIGN=MIDDLE  ALT=\"r%5B1%5D+=+%28-%2810%29%2Bsqrt%28+8100+%29%29%2F2%5C1+=+40\"   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-%2810%29-sqrt%28+8100+%29%29%2F2%5C1+=+-50 ALIGN=MIDDLE  ALT=\"r%5B2%5D+=+%28-%2810%29-sqrt%28+8100+%29%29%2F2%5C1+=+-50\"   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=1r%5E2%2B10r%2B-2000 ALIGN=MIDDLE  ALT=\"1r%5E2%2B10r%2B-2000\"   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=1r%5E2%2B10r%2B-2000+=+1%28r-40%29%2A%28r--50%29 ALIGN=MIDDLE  ALT=\"1r%5E2%2B10r%2B-2000+=+1%28r-40%29%2A%28r--50%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 40, -50.\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+1%2Ax%5E2%2B10%2Ax%2B-2000+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B10%2Ax%2B-2000+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let s= speed of the boat in still water<BR>\n" );
document.write( "The current =3 mi/hr<BR>\n" );
document.write( "we know that d=rt or d/r=t for this problem we must break this up into 2 parts<BR>\n" );
document.write( "(distance upriver)/(rate going upriver)<BR>\n" );
document.write( "+ (distance downriver)/(rate going downriver) = 9 hrs<BR>\n" );
document.write( ":the we know the distance is 60 each way<BR>\n" );
document.write( "the rate going up stream is 60/s-3<BR>\n" );
document.write( "the rate going down stream is 60/s+3<BR>\n" );
document.write( ":<BR>\n" );
document.write( "so we have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60%2F%28s-3%29%2B60%2F%28s%2B3%29=9 ALIGN=MIDDLE  ALT=\"60%2F%28s-3%29%2B60%2F%28s%2B3%29=9\"   DISABLED_style= \"max-width:90%; height:auto;\" >again a quadratic equation<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "multiply each term by (s+3)(s-3)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60%28s%2B3%29%2B60%28s-3%29=9%28s%2B3%29%28s-3%29 ALIGN=MIDDLE  ALT=\"60%28s%2B3%29%2B60%28s-3%29=9%28s%2B3%29%28s-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60s%2B180%2B60s-180=9%28s%5E2-9%29 ALIGN=MIDDLE  ALT=\"60s%2B180%2B60s-180=9%28s%5E2-9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=120s=9s%5E2-81 ALIGN=MIDDLE  ALT=\"120s=9s%5E2-81\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9s%5E2-120s-81=0 ALIGN=MIDDLE  ALT=\"9s%5E2-120s-81=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "drop the negative value<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28s=13.98%2Cs=-.64%29 ALIGN=MIDDLE  ALT=\"system%28s=13.98%2Cs=-.64%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28s=14%29 ALIGN=MIDDLE  ALT=\"highlight%28s=14%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > mph\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<TABLE  BORDER=1>\n" );
document.write( "\n" );
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=as%5E2%2Bbs%2Bc=0 ALIGN=MIDDLE  ALT=\"as%5E2%2Bbs%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9s%5E2%2B-120s%2B-81+=+0 ALIGN=MIDDLE  ALT=\"9s%5E2%2B-120s%2B-81+=+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=s%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"s%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=%28-120%29%5E2-4%2A9%2A-81=17316 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-120%29%5E2-4%2A9%2A-81=17316\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=17316 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--120%2B-sqrt%28+17316+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--120%2B-sqrt%28+17316+%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=s%5B1%5D+=+%28-%28-120%29%2Bsqrt%28+17316+%29%29%2F2%5C9+=+13.9772373998204 ALIGN=MIDDLE  ALT=\"s%5B1%5D+=+%28-%28-120%29%2Bsqrt%28+17316+%29%29%2F2%5C9+=+13.9772373998204\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%5B2%5D+=+%28-%28-120%29-sqrt%28+17316+%29%29%2F2%5C9+=+-0.643904066487102 ALIGN=MIDDLE  ALT=\"s%5B2%5D+=+%28-%28-120%29-sqrt%28+17316+%29%29%2F2%5C9+=+-0.643904066487102\"   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=9s%5E2%2B-120s%2B-81 ALIGN=MIDDLE  ALT=\"9s%5E2%2B-120s%2B-81\"   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=9s%5E2%2B-120s%2B-81+=+9%28s-13.9772373998204%29%2A%28s--0.643904066487102%29 ALIGN=MIDDLE  ALT=\"9s%5E2%2B-120s%2B-81+=+9%28s-13.9772373998204%29%2A%28s--0.643904066487102%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 13.9772373998204, -0.643904066487102.\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+9%2Ax%5E2%2B-120%2Ax%2B-81+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+9%2Ax%5E2%2B-120%2Ax%2B-81+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );