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 #245566 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=245566\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "You are making this too complex in your setup.  Try it this way:\r<BR>\n" );
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document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large r\"> represent the rate of speed on the trip from Denver to SF.  Let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large t\"> represent the amount of elapsed time for the Denver to SF trip.  Then you can say that the return trip was at <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large r\ +\ 40\"> mph and took <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 9\ -\ t\"> hours.  Furthermore, since SF and Denver are, relatively speaking, stationary, if the total round trip distance is 1600 miles, it must be 800 miles each way.\r<BR>\n" );
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document.write( "Now we can describe the outbound trip (in terms of distance equals rate times time) as:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 800 = rt\">\r<BR>\n" );
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document.write( "And the return trip is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 800 = (r\ +\ 40)(9\ -\ t)\">\r<BR>\n" );
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document.write( "Solve each of the above for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large t\"> in terms of everything else:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ t\ =\ \frac{800}{r}\">\r<BR>\n" );
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document.write( "and\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 9\ -\ t\ =\ \frac{800}{r\ +\ 40}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ t\ =\ \frac{9r\ +\ 360\ -\ 800}{r\ +\ 40}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ t\ =\ \frac{9r\ -\ 440}{r\ +\ 40}\">\r<BR>\n" );
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document.write( "Now you have two expressions both equal to <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large t\">.  Set them equal to each other.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{800}{r}\ =\ \frac{9r\ -\ 440}{r\ +\ 40}\">\r<BR>\n" );
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document.write( "Cross-multiply and collect like terms in the LHS, setting everything in the left equal to zero:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 9r^2\ -\ 1240r\ -\ 32000\ =\ 0\">\r<BR>\n" );
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document.write( "Solve the factorable quadratic for <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large r\"> for the average rate of speed on the trip to SF.  Obviously, you will discard any negative root.  Add 40 to get the average rate of speed on the return to Denver.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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document.write( "</font> </SPAN>\n" );
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