document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=205849>Question 205849</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A plane reaches 1200 Km 1 hr earlier, if the speed of the plane is increased by 60km/hr from its initial speed. what is the initial speed of the plane? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #156117 by </B><A HREF=/tutors/aboutme.mpl?userid=AndrewRyan><B>AndrewRyan(3)</B></A><img src=\"/images/stars/iconNewId_16x16.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=AndrewRyan><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=156117\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (x+60) [(1200/x)-1] = 1200<BR>\n" );
document.write( "1200 - x + (72000/x) - 60 = 1200<BR>\n" );
document.write( "x(1200 - 60 - x + (72000/x) = 1200)<BR>\n" );
document.write( "1140x - x^2 + 72000 = 1200x<BR>\n" );
document.write( "-x^2 + 1140x - 1200x + 72000 = 0<BR>\n" );
document.write( "-x^2 - 60x + 72000 = 0<BR>\n" );
document.write( "x^2 + 60x - 72000 = 0<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=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%2B60x%2B-72000+=+0 ALIGN=MIDDLE  ALT=\"1x%5E2%2B60x%2B-72000+=+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=%2860%29%5E2-4%2A1%2A-72000=291600 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2860%29%5E2-4%2A1%2A-72000=291600\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=291600 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+=+%28-60%2B-sqrt%28+291600+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-60%2B-sqrt%28+291600+%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-%2860%29%2Bsqrt%28+291600+%29%29%2F2%5C1+=+240 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%2860%29%2Bsqrt%28+291600+%29%29%2F2%5C1+=+240\"   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-%2860%29-sqrt%28+291600+%29%29%2F2%5C1+=+-300 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%2860%29-sqrt%28+291600+%29%29%2F2%5C1+=+-300\"   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%2B60x%2B-72000 ALIGN=MIDDLE  ALT=\"1x%5E2%2B60x%2B-72000\"   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%2B60x%2B-72000+=+1%28x-240%29%2A%28x--300%29 ALIGN=MIDDLE  ALT=\"1x%5E2%2B60x%2B-72000+=+1%28x-240%29%2A%28x--300%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 240, -300.\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%2B60%2Ax%2B-72000+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B60%2Ax%2B-72000+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "(x - 240)(x + 300)<BR>\n" );
document.write( "x = 240; x = -300  [-300 will be ignored because there is no negative speed]<BR>\n" );
document.write( "x = 240\r<BR>\n" );
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document.write( "checking:<BR>\n" );
document.write( "(240+60) [(1200/240)-1] = 1200<BR>\n" );
document.write( "(300) (5 - 1) = 1200<BR>\n" );
document.write( "(300) (4) = 1200<BR>\n" );
document.write( "1200 = 1200<BR>\n" );
document.write( "x = 240 is a solution </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );