document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=934770>Question 934770</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can someone please help me!!\r<BR>\n" );
document.write( "\n" );
document.write( "It took a small plane 2 h longer to fly 375 mi against the wind than it took the plane to fly the same distance with the wind. the rate of the wind was 25 mph. find the rate of the plane in calm air. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #567789 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39618)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=567789\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> r, rate of plane in calm air<BR>\n" );
document.write( "w, speed of the wind.   Let w=25 mph.<BR>\n" );
document.write( "t, time of travel with the wind<BR>\n" );
document.write( "v, quantity of time in excess of t.  Let v=2 hours.<BR>\n" );
document.write( "q, quantity of distance against the wind.  Let q=375 miles.<BR>\n" );
document.write( "Also, q is the quantity of distance flown with the wind.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "______________________speed___________time______________distance<BR>\n" );
document.write( "AGNST_________________(r-w)___________t+v________________q<BR>\n" );
document.write( "WITH__________________(r+w)____________t_________________q\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The idea in this way is to keep everything in symbols, and save all computations for later.  This is not always necessary.  The only two unknown variables are r and t.  Use the travel rate equation to form two equations for against and for with, the wind.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28%28r-w%29%28t%2Bv%29=q%2C%28r%2Bw%29%2At=q%29 ALIGN=MIDDLE  ALT=\"system%28%28r-w%29%28t%2Bv%29=q%2C%28r%2Bw%29%2At=q%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Solve the system for r, and its value.  This just requires several arithmetic, or algebra steps.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28rt-wt%2Brv-wv=q%2Crt%2Bwt=q%29 ALIGN=MIDDLE  ALT=\"system%28rt-wt%2Brv-wv=q%2Crt%2Bwt=q%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,  but the second equation here was better in its original form.  You want to substitute for t.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The WITH equation is also <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=q%2F%28r%2Bw%29 ALIGN=MIDDLE  ALT=\"t=q%2F%28r%2Bw%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Substitute into \"first\" equation, the AGAINST one.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%28q%2F%28r%2Bw%29%29-w%28q%2F%28r%2Bw%29%29%2Brv-wv=q ALIGN=MIDDLE  ALT=\"r%28q%2F%28r%2Bw%29%29-w%28q%2F%28r%2Bw%29%29%2Brv-wv=q\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=rq-wq%2Brv%28r%2Bw%29-wv%28r%2Bw%29=q%28r%2Bw%29 ALIGN=MIDDLE  ALT=\"rq-wq%2Brv%28r%2Bw%29-wv%28r%2Bw%29=q%28r%2Bw%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=rq-wq%2Bvr%5E2%2Brw-wvr-w%5E2v=qr%2Bqw ALIGN=MIDDLE  ALT=\"rq-wq%2Bvr%5E2%2Brw-wvr-w%5E2v=qr%2Bqw\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=qr%2Bvr%5E2%2Bwr-wvr-w%5E2v-qr-qw=0 ALIGN=MIDDLE  ALT=\"qr%2Bvr%5E2%2Bwr-wvr-w%5E2v-qr-qw=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=vr%5E2%2Bqr%2Bwr-wvr-qr-w%5E2v-qw=0 ALIGN=MIDDLE  ALT=\"vr%5E2%2Bqr%2Bwr-wvr-qr-w%5E2v-qw=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=vr%5E2%2B%28q%2Bw-wv-q%29r-w%5E2v-qw=0 ALIGN=MIDDLE  ALT=\"vr%5E2%2B%28q%2Bw-wv-q%29r-w%5E2v-qw=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28vr%5E2%2B%28w-wv%29r-%28w%5E2v%2Bqw%29=0%29 ALIGN=MIDDLE  ALT=\"highlight_green%28vr%5E2%2B%28w-wv%29r-%28w%5E2v%2Bqw%29=0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You could keep going completely in symbols, but now would be a good place for the next step to plug in the known values, AND THEN finish the solving of this quadratic equation for r.  Note, the question asks for r, the rate of the plane in calm air, and r is the only variable UNKNOWN in this quadratic equation.  You would then use general solution ....\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );