document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=172797>Question 172797</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A plane makes a 240-mile trip against a head wind in 1 hour and 30 minutes and returns, with a tail wind of the same speed, in 1 hour.  What is the speed of the wind and what is the speed of the plane? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #127638 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=127638\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let w=speed of wind and p=speed of plane\r<BR>\n" );
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document.write( "Note: 1 hour and 30 minutes = 1.5 hours (ie 1 and a half hours)\r<BR>\n" );
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document.write( "Against Wind:\r<BR>\n" );
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document.write( "Going against the wind will slow you down. So this means that the speeds plane against the wind is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=p-w ALIGN=MIDDLE  ALT=\"r=p-w\"   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=d=rt ALIGN=MIDDLE  ALT=\"d=rt\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the distance rate time formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=240=%28p-w%291.5 ALIGN=MIDDLE  ALT=\"240=%28p-w%291.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=240 ALIGN=MIDDLE  ALT=\"d=240\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=p-w ALIGN=MIDDLE  ALT=\"r=p-w\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=1.5 ALIGN=MIDDLE  ALT=\"t=1.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > (this is the time it takes to go against the wind)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=240%2F1.5=p-w ALIGN=MIDDLE  ALT=\"240%2F1.5=p-w\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.5 ALIGN=MIDDLE  ALT=\"1.5\"   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=160=p-w ALIGN=MIDDLE  ALT=\"160=p-w\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%2B160=p ALIGN=MIDDLE  ALT=\"w%2B160=p\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add \"w\" to both sides to isolate \"p\".\r<BR>\n" );
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document.write( "So after isolating \"p\", we get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=w%2B160 ALIGN=MIDDLE  ALT=\"p=w%2B160\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "With Wind:\r<BR>\n" );
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document.write( "In contrast, going with the wind will speed you up. So this means that the speeds plane with the wind is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=p%2Bw ALIGN=MIDDLE  ALT=\"r=p%2Bw\"   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=d=rt ALIGN=MIDDLE  ALT=\"d=rt\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the distance rate time formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=240=%28p%2Bw%291 ALIGN=MIDDLE  ALT=\"240=%28p%2Bw%291\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=240 ALIGN=MIDDLE  ALT=\"d=240\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=p%2Bw ALIGN=MIDDLE  ALT=\"r=p%2Bw\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=1 ALIGN=MIDDLE  ALT=\"t=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > (this is the time it takes to go with the wind)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=240=p%2Bw ALIGN=MIDDLE  ALT=\"240=p%2Bw\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=240=w%2B160%2Bw ALIGN=MIDDLE  ALT=\"240=w%2B160%2Bw\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=w%2B160 ALIGN=MIDDLE  ALT=\"p=w%2B160\"   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=240-160=w%2Bw ALIGN=MIDDLE  ALT=\"240-160=w%2Bw\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 160 from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=80=2w ALIGN=MIDDLE  ALT=\"80=2w\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=80%2F2=w ALIGN=MIDDLE  ALT=\"80%2F2=w\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to isolate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w ALIGN=MIDDLE  ALT=\"w\"   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=40=w ALIGN=MIDDLE  ALT=\"40=w\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce\r<BR>\n" );
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document.write( "So the first answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=40 ALIGN=MIDDLE  ALT=\"w=40\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This means that the speed of the wind is 40 mph\r<BR>\n" );
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document.write( "--------------------------------------------\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=w%2B160 ALIGN=MIDDLE  ALT=\"p=w%2B160\"   DISABLED_style= \"max-width:90%; height:auto;\" > Go back to the previously isolated equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=40%2B160 ALIGN=MIDDLE  ALT=\"p=40%2B160\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=40 ALIGN=MIDDLE  ALT=\"w=40\"   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=p=200 ALIGN=MIDDLE  ALT=\"p=200\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add\r<BR>\n" );
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document.write( "So the second answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=200 ALIGN=MIDDLE  ALT=\"w=200\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This means that the speed of the plane is 200 mph\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So the solutions are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=40 ALIGN=MIDDLE  ALT=\"w=40\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=200 ALIGN=MIDDLE  ALT=\"p=200\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This means that the speed of the wind is 40 miles per hour and the speed of the plane is 200 miles per hour.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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