document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=170780>Question 170780</A>: <I><SPAN STYLE=\"word-break: break-all;\"> At 10:00 AM, a snowstorm is 250 miles west of St. Louis.  The storm travels 150 miles eastward at a constant rate, and then its speed decreases by 5 miles per hour.  If the storm reaches St. Louis at 8:00 PM, what was the storm's original speed? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #126144 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=126144\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> distance equals rate times time<BR>\n" );
document.write( "lets call the 1st 150 miles rate=r and time=t<BR>\n" );
document.write( "and we will call the last 100 miles rate r-5 and time 10-t<BR>\n" );
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document.write( "150=rt--->t=150/r.....eq 1<BR>\n" );
document.write( "100=(r-5)(10-t).......eq 2<BR>\n" );
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document.write( "take value of t from eq 1 and plug it into eq 2<BR>\n" );
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document.write( "100=(r-5)(10-(150/r))--->100=(r-5)((10r-150)/r)...multiply both sides by r<BR>\n" );
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document.write( "100r=(r-5)(10r-150)<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100r=10r%5E2-150r-50r%2B750 ALIGN=MIDDLE  ALT=\"100r=10r%5E2-150r-50r%2B750\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10r%5E2-300r%2B750=0 ALIGN=MIDDLE  ALT=\"10r%5E2-300r%2B750=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >divide by 10<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E2-30r%2B75=0 ALIGN=MIDDLE  ALT=\"r%5E2-30r%2B75=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "r=27.25 and 2.75......throw out the 2.75 rate because r-5 is negative.<BR>\n" );
document.write( "so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28r=27.25%29 ALIGN=MIDDLE  ALT=\"highlight%28r=27.25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >mph-the original speed of the storm\r<BR>\n" );
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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=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%5E2%2B-30x%2B75+=+0 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-30x%2B75+=+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=x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"x%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=%28-30%29%5E2-4%2A1%2A75=600 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-30%29%5E2-4%2A1%2A75=600\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=600 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--30%2B-sqrt%28+600+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--30%2B-sqrt%28+600+%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=x%5B1%5D+=+%28-%28-30%29%2Bsqrt%28+600+%29%29%2F2%5C1+=+27.2474487139159 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-30%29%2Bsqrt%28+600+%29%29%2F2%5C1+=+27.2474487139159\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+%28-%28-30%29-sqrt%28+600+%29%29%2F2%5C1+=+2.75255128608411 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-30%29-sqrt%28+600+%29%29%2F2%5C1+=+2.75255128608411\"   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=1x%5E2%2B-30x%2B75 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-30x%2B75\"   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=1x%5E2%2B-30x%2B75+=+1%28x-27.2474487139159%29%2A%28x-2.75255128608411%29 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-30x%2B75+=+1%28x-27.2474487139159%29%2A%28x-2.75255128608411%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 27.2474487139159, 2.75255128608411.\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%2B-30%2Ax%2B75+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-30%2Ax%2B75+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( " </SPAN>\n" );
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