document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=209818>Question 209818</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A six-passenger plane cruises at 180 mph in calm air. If the plane flies 7 miles with the wind in the same amount of time as it flies 5 miles against the wind, then what is the speed of the wind?				 \r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #158602 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=158602\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Using <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+rt ALIGN=MIDDLE  ALT=\"d+=+rt\"   DISABLED_style= \"max-width:90%; height:auto;\" > where d = distance, r = rate(speed), and t = time of travel, we can express the two legs (out and return) of the airplane.<BR>\n" );
document.write( "For the outbound leg, the speed of the airplane can be expressed as:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5B1%5D+=+180%2Bw ALIGN=MIDDLE  ALT=\"r%5B1%5D+=+180%2Bw\"   DISABLED_style= \"max-width:90%; height:auto;\" > The speed is faster because the wind speed is added to that of the air plane when flying with the wind.<BR>\n" );
document.write( "For the return leg, the speed of the airplane can be expressed as:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5B2%5D+=+180-w ALIGN=MIDDLE  ALT=\"r%5B2%5D+=+180-w\"   DISABLED_style= \"max-width:90%; height:auto;\" > The speed is slower because the wind speed is subtracted from that of the airplane when flying against the wind.<BR>\n" );
document.write( "Now the distance traveled is given as:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B1%5D+=+7 ALIGN=MIDDLE  ALT=\"d%5B1%5D+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B2%5D+=+5 ALIGN=MIDDLE  ALT=\"d%5B2%5D+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the time of travel, t, is the same for both legs.<BR>\n" );
document.write( "So, we have enough data to set up our two equations.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B1%5D+=+r%5B1%5D%2At ALIGN=MIDDLE  ALT=\"d%5B1%5D+=+r%5B1%5D%2At\"   DISABLED_style= \"max-width:90%; height:auto;\" > and...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5B2%5D+=+r%5B2%5D%2At ALIGN=MIDDLE  ALT=\"d%5B2%5D+=+r%5B2%5D%2At\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Making the appropriate substitutions, we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7+=+%28180%2Bw%29%2At ALIGN=MIDDLE  ALT=\"7+=+%28180%2Bw%29%2At\"   DISABLED_style= \"max-width:90%; height:auto;\" > and...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5+=+%28180-w%29%2At ALIGN=MIDDLE  ALT=\"5+=+%28180-w%29%2At\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Solving both of the equations for t, we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+7%2F%28180%2Bw%29 ALIGN=MIDDLE  ALT=\"t+=+7%2F%28180%2Bw%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+5%2F%28180-w%29 ALIGN=MIDDLE  ALT=\"t+=+5%2F%28180-w%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now since t = t we can set these two equations equal to each other to get...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2F%28180%2Bw%29+=+5%2F%28180-w%29 ALIGN=MIDDLE  ALT=\"7%2F%28180%2Bw%29+=+5%2F%28180-w%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now we can solve for w, the wind speed.<BR>\n" );
document.write( "Cross-multiply.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%28180-w%29+=+5%28180%2Bw%29 ALIGN=MIDDLE  ALT=\"7%28180-w%29+=+5%28180%2Bw%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1260-7w+=+900%2B5w ALIGN=MIDDLE  ALT=\"1260-7w+=+900%2B5w\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 7w to both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1260+=+900%2B12w ALIGN=MIDDLE  ALT=\"1260+=+900%2B12w\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 900 from both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=360+=+12w ALIGN=MIDDLE  ALT=\"360+=+12w\"   DISABLED_style= \"max-width:90%; height:auto;\" > Finally, divide both sides by 12.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30+=+w ALIGN=MIDDLE  ALT=\"30+=+w\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w+=+30 ALIGN=MIDDLE  ALT=\"w+=+30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The wind speed is 30mph.  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );