document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=342957>Question 342957</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Trying to help my son with Algebra II, and I just can't remember!\r<BR>\n" );
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document.write( "Plane flies roundtrip from Denver to San Francisco a total of 1600 miles.  Trip time is 9 hours.  Return trip from San Francisco, the plane averages 40 mph faster than the outbound flight.  What is the average speed to San Fran and back?  <BR>\n" );
document.write( "X1 = Avg speed out in mph<BR>\n" );
document.write( "X2 = Avg speed back in mph<BR>\n" );
document.write( "Y1 = time out in hours<BR>\n" );
document.write( "Y2 = time back in hours<BR>\n" );
document.write( "1600 Miles = X1*Y1 + X2*Y2<BR>\n" );
document.write( "Y2= 9-Y1<BR>\n" );
document.write( "X2 = X1 + 40 mph<BR>\n" );
document.write( "X1 = 800/Y1\r<BR>\n" );
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document.write( "I set up to solve for mph, using the substitutions I've identified, and get lost... </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #245448 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=245448\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Plane flies roundtrip from Denver to San Francisco a total of 1600 miles. Trip time is 9 hours. Return trip from San Francisco, the plane averages 40 mph faster than the outbound flight. What is the average speed to San Fran and back?<BR>\n" );
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document.write( "Is 9 hours the time for the round trip?  800 miles each way?  If so:<BR>\n" );
document.write( "The average overall is 1600/9 =~ 177.8 mph<BR>\n" );
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document.write( "If you want the avg speed for each half of the trip:<BR>\n" );
document.write( "d = rt<BR>\n" );
document.write( "t = d/r<BR>\n" );
document.write( "9 = 800/r + 800/(r+40)<BR>\n" );
document.write( "9*r*(r+40) = 800(r+40) + 800r<BR>\n" );
document.write( "9r^2 + 360r = 800r + 3200 + 800r = 1600r + 3200<BR>\n" );
document.write( "9r^2 - 1240r - 3200 = 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=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-1240x%2B-3200+=+0 ALIGN=MIDDLE  ALT=\"9x%5E2%2B-1240x%2B-3200+=+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=%28-1240%29%5E2-4%2A9%2A-3200=1652800 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-1240%29%5E2-4%2A9%2A-3200=1652800\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=1652800 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--1240%2B-sqrt%28+1652800+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--1240%2B-sqrt%28+1652800+%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-%28-1240%29%2Bsqrt%28+1652800+%29%29%2F2%5C9+=+140.311816355503 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-1240%29%2Bsqrt%28+1652800+%29%29%2F2%5C9+=+140.311816355503\"   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-%28-1240%29-sqrt%28+1652800+%29%29%2F2%5C9+=+-2.53403857772532 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-1240%29-sqrt%28+1652800+%29%29%2F2%5C9+=+-2.53403857772532\"   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-1240x%2B-3200 ALIGN=MIDDLE  ALT=\"9x%5E2%2B-1240x%2B-3200\"   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-1240x%2B-3200+=+%28x-140.311816355503%29%2A%28x--2.53403857772532%29 ALIGN=MIDDLE  ALT=\"9x%5E2%2B-1240x%2B-3200+=+%28x-140.311816355503%29%2A%28x--2.53403857772532%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 140.311816355503, -2.53403857772532.\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-1240%2Ax%2B-3200+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+9%2Ax%5E2%2B-1240%2Ax%2B-3200+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "r = x (Ignore the negative solution)<BR>\n" );
document.write( "r =~ 140 going<BR>\n" );
document.write( "r + 40 =~ 180 returning<BR>\n" );
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document.write( "</TD></TR></TABLE>\n" );