document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=769537>Question 769537</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Flying against the wind, it took a pilot 1/2 hour longer to travel 500 miles than it took flying with the wind.  The rate of the plane in calm air is 225 mph.  Find the rate of the wind. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #468915 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=468915\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+w+ ALIGN=MIDDLE  ALT=\"+w+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the rate of the wind<BR>\n" );
document.write( "Flying with the wind, the plane's rate is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+225+%2B+w+ ALIGN=MIDDLE  ALT=\"+225+%2B+w+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Flying against the wind, the plane's rate is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+225+-+w+ ALIGN=MIDDLE  ALT=\"+225+-+w+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "Equation flying with the wind:<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+500+=+%28+225+%2B+w+%29%2At+ ALIGN=MIDDLE  ALT=\"+500+=+%28+225+%2B+w+%29%2At+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Flying against the wind:<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+500+=+%28+225+-+w+%29%2A%28+t+%2B+.5+%29+ ALIGN=MIDDLE  ALT=\"+500+=+%28+225+-+w+%29%2A%28+t+%2B+.5+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "------------------------------<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+500+=+225t+-+w%2At+%2B+.5%2A225+-+.5w+ ALIGN=MIDDLE  ALT=\"+500+=+225t+-+w%2At+%2B+.5%2A225+-+.5w+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+w%2At+%2B+.5w+=+225t+%2B+112.5+-+500+ ALIGN=MIDDLE  ALT=\"+w%2At+%2B+.5w+=+225t+%2B+112.5+-+500+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+w%2A%28+t+%2B+.5+%29+=+225t+-+387.5+ ALIGN=MIDDLE  ALT=\"+w%2A%28+t+%2B+.5+%29+=+225t+-+387.5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-------------------------------<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+500+=+225t+%2B+w%2At+ ALIGN=MIDDLE  ALT=\"+500+=+225t+%2B+w%2At+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+w%2At+=+500+-+225t+ ALIGN=MIDDLE  ALT=\"+w%2At+=+500+-+225t+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+w+=+500%2Ft+-+225+ ALIGN=MIDDLE  ALT=\"+w+=+500%2Ft+-+225+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------------------<BR>\n" );
document.write( "Substitute (1) into (2)<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+500%2Ft+-+225+%29%2A%28+t+%2B+.5+%29+=+225t+-+387.5+ ALIGN=MIDDLE  ALT=\"+%28+500%2Ft+-+225+%29%2A%28+t+%2B+.5+%29+=+225t+-+387.5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+500+-+225t+%2B+250%2Ft+-+112.5+=+225t+-+387.5+ ALIGN=MIDDLE  ALT=\"+500+-+225t+%2B+250%2Ft+-+112.5+=+225t+-+387.5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+250%2Ft+=+450t+-+775+ ALIGN=MIDDLE  ALT=\"+250%2Ft+=+450t+-+775+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+250+=+450t%5E2+-+775t+ ALIGN=MIDDLE  ALT=\"+250+=+450t%5E2+-+775t+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+450t%5E2+-+775t+-+250+=+0+ ALIGN=MIDDLE  ALT=\"+450t%5E2+-+775t+-+250+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+18t%5E2+-+31t+-+10+=+0+ ALIGN=MIDDLE  ALT=\"+18t%5E2+-+31t+-+10+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Use quadratic formula<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"+t+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+18+ ALIGN=MIDDLE  ALT=\"+a+=+18+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+-31+ ALIGN=MIDDLE  ALT=\"+b+=+-31+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+c+=+-10+ ALIGN=MIDDLE  ALT=\"+c+=+-10+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+%28-%28-31%29+%2B-+sqrt%28+%28-31%29%5E2+-+4%2A18%2A%28-10%29+%29%29+%2F+%282%2A18%29+ ALIGN=MIDDLE  ALT=\"+t+=+%28-%28-31%29+%2B-+sqrt%28+%28-31%29%5E2+-+4%2A18%2A%28-10%29+%29%29+%2F+%282%2A18%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+%28+31+%2B-+sqrt%28+961+%2B+720+%29%29+%2F+36+ ALIGN=MIDDLE  ALT=\"+t+=+%28+31+%2B-+sqrt%28+961+%2B+720+%29%29+%2F+36+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+%28+31+%2B-+sqrt%28+1681+%29%29+%2F+36+ ALIGN=MIDDLE  ALT=\"+t+=+%28+31+%2B-+sqrt%28+1681+%29%29+%2F+36+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+%28+31+%2B+41+%29+%2F+36+ ALIGN=MIDDLE  ALT=\"+t+=+%28+31+%2B+41+%29+%2F+36+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( can't use the negative root )<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+72%2F36+ ALIGN=MIDDLE  ALT=\"+t+=+72%2F36+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+2+ ALIGN=MIDDLE  ALT=\"+t+=+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and, since<BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+500+=+%28+225+%2B+w+%29%2At+ ALIGN=MIDDLE  ALT=\"+500+=+%28+225+%2B+w+%29%2At+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+500+=+%28+225+%2B+w+%29%2A2+ ALIGN=MIDDLE  ALT=\"+500+=+%28+225+%2B+w+%29%2A2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+450+%2B+2w+=+500+ ALIGN=MIDDLE  ALT=\"+450+%2B+2w+=+500+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2w+=+50+ ALIGN=MIDDLE  ALT=\"+2w+=+50+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+w+=+25+ ALIGN=MIDDLE  ALT=\"+w+=+25+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The rate of the wind is 25 mi/hr<BR>\n" );
document.write( "check:<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+500+=+%28+225+-+w+%29%2A%28+t+%2B+.5+%29+ ALIGN=MIDDLE  ALT=\"+500+=+%28+225+-+w+%29%2A%28+t+%2B+.5+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+500+=+%28+225+-+25+%29%2A%28+2+%2B+.5+%29+ ALIGN=MIDDLE  ALT=\"+500+=+%28+225+-+25+%29%2A%28+2+%2B+.5+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+500+=+200%2A2.5+ ALIGN=MIDDLE  ALT=\"+500+=+200%2A2.5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+500+=+500+ ALIGN=MIDDLE  ALT=\"+500+=+500+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );