document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=123257>Question 123257</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hank travels home to Smithville every weekend from Ottawa.The distance each way is 800km. Anxious to return home, he decides to increase his speed by 20km/h and realizes that he arrives home two hours earlier than the time it took him to travel from home to Ottawa. How long does the trip to Ottawa usually take? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #90500 by </B><A HREF=/tutors/aboutme.mpl?userid=rajagopalan><B>rajagopalan(174)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rajagopalan><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=rajagopalan><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=90500\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hank travels home to Smithville every weekend from Ottawa.The distance each way is 800km. Anxious to return home, he decides to increase his speed by 20km/h and realizes that he arrives home two hours earlier than the time it took him to travel from home to Ottawa. How long does the trip to Ottawa usually take?\r<BR>\n" );
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document.write( "Let the normal speed=x kmph<BR>\n" );
document.write( "Time for onward trip =dist/speed=800/x .. .. .. .. ..A<BR>\n" );
document.write( "Time for return trip=dist/speed=800/(x+20).. .. .. ..B\r<BR>\n" );
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document.write( "Difference in times =A-B<BR>\n" );
document.write( "gives us:<BR>\n" );
document.write( "(800/x)-(800/(x+20))=2<BR>\n" );
document.write( "taking x(x+20) as LCM, we get the quadratic 2x^2+40x-16000=0<BR>\n" );
document.write( "which boils down to x^2+40x-8000 <BR>\n" );
document.write( "solution is:\r<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=1x%5E2%2B20x%2B-8000+=+0 ALIGN=MIDDLE  ALT=\"1x%5E2%2B20x%2B-8000+=+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=%2820%29%5E2-4%2A1%2A-8000=32400 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2820%29%5E2-4%2A1%2A-8000=32400\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=32400 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+=+%28-20%2B-sqrt%28+32400+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-20%2B-sqrt%28+32400+%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-%2820%29%2Bsqrt%28+32400+%29%29%2F2%5C1+=+80 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%2820%29%2Bsqrt%28+32400+%29%29%2F2%5C1+=+80\"   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-%2820%29-sqrt%28+32400+%29%29%2F2%5C1+=+-100 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%2820%29-sqrt%28+32400+%29%29%2F2%5C1+=+-100\"   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%2B20x%2B-8000 ALIGN=MIDDLE  ALT=\"1x%5E2%2B20x%2B-8000\"   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%2B20x%2B-8000+=+%28x-80%29%2A%28x--100%29 ALIGN=MIDDLE  ALT=\"1x%5E2%2B20x%2B-8000+=+%28x-80%29%2A%28x--100%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 80, -100.\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%2B20%2Ax%2B-8000+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B20%2Ax%2B-8000+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "we get x=80<BR>\n" );
document.write( "at speed of 80 time=800/80=10hours<BR>\n" );
document.write( "at speed 80+20 time=80/100=8 hours<BR>\n" );
document.write( "then 10-8 hours=2 hours <BR>\n" );
document.write( "okay\r<BR>\n" );
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document.write( " </SPAN>\n" );
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