document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=164682>Question 164682</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Dave and Sandy fly from Philly to Chicago, it takes 2 hours to go west and 1 and a half hours to fly east. The trip is 780 one way. If the wind speed is the same on each trip, find the speed of the wind and find the speed of the plane in the still air. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #121343 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><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=121343\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> D = 780 miles<BR>\n" );
document.write( "let A = airspeed<BR>\n" );
document.write( "let W = windspeed<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "since it takes more time to go west than east, it's fair to say that the wind was against the airplane going west and with the airplane going east.<BR>\n" );
document.write( "TW = time going west = 2 hours<BR>\n" );
document.write( "TE = time going east = 1.5 hours<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "since the rate of travel times the duration of travel equals the distance, the equations for going west and going east are:<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "TW * (A-W) = 780 <BR>\n" );
document.write( "TE * (A+W) = 780 <BR>\n" );
document.write( "-----<BR>\n" );
document.write( "substituting for TW and TE makes the equations become:<BR>\n" );
document.write( "2 * (A-W) = 780 (original first equation)<BR>\n" );
document.write( "1.5 * (A+W) = 780 (original second equation)<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "since both equations equal 780, then they are equal to each other (transitive property of algebraic operations).<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "2 * (A-W) = 1.5 * (A+W)<BR>\n" );
document.write( "removing parentheses:<BR>\n" );
document.write( "2*A - 2*W = 1.5*A + 1.5*W<BR>\n" );
document.write( "subtracting 1.5*A from both sides of equation and adding 2*W to both sides of equation:<BR>\n" );
document.write( "2*A - 1.5*A = 1.5*W + 2*W<BR>\n" );
document.write( "combining like terms:<BR>\n" );
document.write( ".5*A = 3.5*W<BR>\n" );
document.write( "multiplying both sides of equation by 2:<BR>\n" );
document.write( "A = 7*W<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "original first equation is:<BR>\n" );
document.write( "2 * (A-W) = 780<BR>\n" );
document.write( "removing parentheses:<BR>\n" );
document.write( "2*A - 2*W = 780<BR>\n" );
document.write( "substituting 7*W for A:<BR>\n" );
document.write( "2*7*W - 2*W = 780<BR>\n" );
document.write( "simplifying and combining like terms:<BR>\n" );
document.write( "12*W = 780<BR>\n" );
document.write( "dividing both sides by 12:<BR>\n" );
document.write( "W = 65<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "original second equation is:<BR>\n" );
document.write( "1.5 * (A+W) = 780<BR>\n" );
document.write( "removing parentheses:<BR>\n" );
document.write( "1.5*A + 1.5*W = 780<BR>\n" );
document.write( "substituting 65 for W:<BR>\n" );
document.write( "1.5*A + 1.5*65 = 780<BR>\n" );
document.write( "simplifying:<BR>\n" );
document.write( "1.5*A + 97.5 = 780<BR>\n" );
document.write( "subtracting 97.5 from both sides of equation:<BR>\n" );
document.write( "1.5*A = 780 - 97.5<BR>\n" );
document.write( "simplifying:<BR>\n" );
document.write( "1.5*A = 682.5<BR>\n" );
document.write( "dividing both sides of equation by 1.5<BR>\n" );
document.write( "A = 682.5/1.5<BR>\n" );
document.write( "simplifying:<BR>\n" );
document.write( "A = 455<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "original first and second equations are:<BR>\n" );
document.write( "2 * (A-W) = 780 (original first equation)<BR>\n" );
document.write( "1.5 * (A+W) = 780 (original second equation)<BR>\n" );
document.write( "substituting 455 for A and 65 for W in original first equation:<BR>\n" );
document.write( "2 * (455-65) = 780<BR>\n" );
document.write( "simplifying:<BR>\n" );
document.write( "2*390 = 780<BR>\n" );
document.write( "780 = 780<BR>\n" );
document.write( "first equation is good<BR>\n" );
document.write( "substituting 455 for A and 65 for W in original second equation:<BR>\n" );
document.write( "1.5 * (455+65) = 780<BR>\n" );
document.write( "simplifying:<BR>\n" );
document.write( "1.5 * (520) = 780<BR>\n" );
document.write( "780 = 780<BR>\n" );
document.write( "second equation is good.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "answer is:<BR>\n" );
document.write( "Airplane speed is 455 miles per hour.<BR>\n" );
document.write( "Wind speed is 65 miles per hour.\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );