document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=750065>Question 750065</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Miami and Pittsburg are 1000 miles apart. A plane flew into a 50mph headwind from miami to pittsburg. on the return flight the 50mph wind became a tailwind. The lane was in the air a total of 4.5 hrs. for the roundtrip. what would have been the planes average speed without the wind? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #456358 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=456358\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Miami and Pittsburg are 1000 miles apart. A plane flew into a 50mph headwind from miami to pittsburg. on the return flight the 50mph wind became a tailwind. The lane was in the air a total of 4.5 hrs. for the roundtrip. what would have been the planes average speed without the wind?<BR>\n" );
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document.write( "p = plane's airspeed<BR>\n" );
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document.write( "1000/(p - 50) + 1000/(p + 50) = 4.5<BR>\n" );
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document.write( "1000*(2p) = 4.5*(p^2 - 2500)<BR>\n" );
document.write( "4000p = 9p^2 - 22500<BR>\n" );
document.write( "9p^2 - 4000p - 22500 = 0<BR>\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=solve_quadratic_equation.solver>SOLVE quadratic equation (work shown, graph etc)</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=9x%5E2%2B-4000x%2B-22500+=+0 ALIGN=MIDDLE  ALT=\"9x%5E2%2B-4000x%2B-22500+=+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=%28-4000%29%5E2-4%2A9%2A-22500=16810000 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-4000%29%5E2-4%2A9%2A-22500=16810000\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=16810000 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--4000%2B-sqrt%28+16810000+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--4000%2B-sqrt%28+16810000+%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-%28-4000%29%2Bsqrt%28+16810000+%29%29%2F2%5C9+=+450 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-4000%29%2Bsqrt%28+16810000+%29%29%2F2%5C9+=+450\"   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-%28-4000%29-sqrt%28+16810000+%29%29%2F2%5C9+=+-5.55555555555556 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-4000%29-sqrt%28+16810000+%29%29%2F2%5C9+=+-5.55555555555556\"   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=9x%5E2%2B-4000x%2B-22500 ALIGN=MIDDLE  ALT=\"9x%5E2%2B-4000x%2B-22500\"   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=9x%5E2%2B-4000x%2B-22500+=+%28x-450%29%2A%28x--5.55555555555556%29 ALIGN=MIDDLE  ALT=\"9x%5E2%2B-4000x%2B-22500+=+%28x-450%29%2A%28x--5.55555555555556%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 450, -5.55555555555556.\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-4000%2Ax%2B-22500+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+9%2Ax%5E2%2B-4000%2Ax%2B-22500+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "Ignore the negative solution,<BR>\n" );
document.write( "p = 450 mi/hr<BR>\n" );
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document.write( "with no wind, the avg = 450 mi/hr<BR>\n" );
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