document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=153165>Question 153165</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Making a round trip from Fairview to Casterville, a distance of 20 miles, a pilot faces a 30mph head wind one way and a 30mph tail wind on the return trip.  The return trip takes 45 minutes less than the outbound journey.  Find the speed of the plane in still air\r<BR>\n" );
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document.write( "from Fair/Cast distance=10miles; rate = (r-30); time = t<BR>\n" );
document.write( "from Cast/Fair distnace= 10miles; rate = (r+30); time = t -45<BR>\n" );
document.write( "the total distance is 20 miles\r<BR>\n" );
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document.write( "so 10 = t(r-30)<BR>\n" );
document.write( "   10 = (r+30)(t-45)\r<BR>\n" );
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document.write( "the two variables are throwing me off, somethings wrong in my setup??\r<BR>\n" );
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document.write( "Thanks for your help. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #112669 by </B><A HREF=/tutors/aboutme.mpl?userid=orca><B>orca(409)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=orca><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=112669\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There is only a small mistake in the second equation. It is the unit of time.<BR>\n" );
document.write( "Note that the unit for the speed of the wind is miles/hour. So you need to convert 45 minutes into 3/4 hours<BR>\n" );
document.write( "So the simultaneous equations become:<BR>\n" );
document.write( "10 = t(r-30) ................(1)<BR>\n" );
document.write( "10 = (r+30)(t-3/4) ...........(2)\r<BR>\n" );
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document.write( "From equation (1), we have<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+10%2F%28r-30%29 ALIGN=MIDDLE  ALT=\"t+=+10%2F%28r-30%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substituting it into equation (2), we have<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10+=+%28r%2B30%29%2810%2F%28r-30%29-3%2F4%29 ALIGN=MIDDLE  ALT=\"10+=+%28r%2B30%29%2810%2F%28r-30%29-3%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Solving for the above equation, we obtain<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10+=+10%28r%2B30%29%2F%28r-30%29-3%28r%2B30%29%2F4%29 ALIGN=MIDDLE  ALT=\"10+=+10%28r%2B30%29%2F%28r-30%29-3%28r%2B30%29%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2A4%28r-30%29+=+4%2A10%28r%2B30%29-3%28r%2B30%29%28r-30%29 ALIGN=MIDDLE  ALT=\"10%2A4%28r-30%29+=+4%2A10%28r%2B30%29-3%28r%2B30%29%28r-30%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiplying both sides by 4(r-30)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40r-1200=40r%2B1200+-3%28r%5E2-30%5E2%29 ALIGN=MIDDLE  ALT=\"40r-1200=40r%2B1200+-3%28r%5E2-30%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=40r-1200=40r%2B1200+-3%28r%5E2-900%29 ALIGN=MIDDLE  ALT=\"40r-1200=40r%2B1200+-3%28r%5E2-900%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40r-1200=40r%2B1200+-3r%5E2%2B2700%29 ALIGN=MIDDLE  ALT=\"40r-1200=40r%2B1200+-3r%5E2%2B2700%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3r%5E2=2700%2B1200%2B1200 ALIGN=MIDDLE  ALT=\"3r%5E2=2700%2B1200%2B1200\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3r%5E2=5100 ALIGN=MIDDLE  ALT=\"3r%5E2=5100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E2=1700 ALIGN=MIDDLE  ALT=\"r%5E2=1700\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+10sqrt%2817%29 ALIGN=MIDDLE  ALT=\"r+=+10sqrt%2817%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+41.23+ ALIGN=MIDDLE  ALT=\"r+=+41.23+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
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