document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1103240>Question 1103240</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A plane travels at a speed of 180 mph in still air . Flying with a tailwind the plane is clocked over a of distance of 900 miles. Flying against a headwind it takes 2 hours longer to complete the return trip. What was the wind velocity? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #717943 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39629)</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=717943\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28r=180%2Cd=900%2Ch=2%2Cw=unknownWindSpeed%29 ALIGN=MIDDLE  ALT=\"system%28r=180%2Cd=900%2Ch=2%2Cw=unknownWindSpeed%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "h is for time difference\r<BR>\n" );
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document.write( "                  SPEEDS   TIMES      DISTANCE\r\n" );
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document.write( "WITH WIND          r+w     d/(r+w)      d\r\n" );
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document.write( "AGAINST WIND       r-w     d/(r-w)      d\r\n" );
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document.write( "DIFFERENCE                  h\r\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28d%2F%28r-w%29-d%2F%28r%2Bw%29=h%29 ALIGN=MIDDLE  ALT=\"highlight_green%28d%2F%28r-w%29-d%2F%28r%2Bw%29=h%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Solve for w.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%28r%2Bw%29-d%28r-w%29=h%28r%5E2-w%5E2%29 ALIGN=MIDDLE  ALT=\"d%28r%2Bw%29-d%28r-w%29=h%28r%5E2-w%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dr%2Bdw-dr%2Bdw=hr%5E2-hw%5E2 ALIGN=MIDDLE  ALT=\"dr%2Bdw-dr%2Bdw=hr%5E2-hw%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=hw%5E2%2B2dw-hr%5E2=0 ALIGN=MIDDLE  ALT=\"hw%5E2%2B2dw-hr%5E2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Using general solution for quadratic equation, and not assuming the quadratic would be factorable,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=%28-2d%2B-+sqrt%28%282d%29%5E2%2B4h%2Ahr%5E2%29%29%2F%282h%29 ALIGN=MIDDLE  ALT=\"w=%28-2d%2B-+sqrt%28%282d%29%5E2%2B4h%2Ahr%5E2%29%29%2F%282h%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=%28-2d%2B-+sqrt%284d%5E2%2B4h%5E2r%5E2%29%29%2F%282h%29 ALIGN=MIDDLE  ALT=\"w=%28-2d%2B-+sqrt%284d%5E2%2B4h%5E2r%5E2%29%29%2F%282h%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28w=%28-d%2B-+sqrt%28d%5E2%2Bh%5E2r%5E2%29%29%2Fh%29 ALIGN=MIDDLE  ALT=\"highlight%28w=%28-d%2B-+sqrt%28d%5E2%2Bh%5E2r%5E2%29%29%2Fh%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >-------the PLUS form will probably be what you want.  Substitute the given values now and evaluate both solutions for w, and decide which makes sense.\r<BR>\n" );
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document.write( "Substitute the given values into the formula for w, and should find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28w=34.7%2A%28miles%2Fhour%29%29 ALIGN=MIDDLE  ALT=\"highlight%28w=34.7%2A%28miles%2Fhour%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
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