document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=120519>Question 120519</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A plane flies 720 mi against a steady 30-mi/h headwind and then returns to the same point with the wind. If the entire trip takes 10 h, what is the plane’s speed in still air? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #88360 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=88360\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let r be the speed in still air, in accordance with rule one for word problems: Set the variable equal to the thing you want to know.\r<BR>\n" );
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document.write( "Air speed against the wind would then be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r-30 ALIGN=MIDDLE  ALT=\"r-30\"   DISABLED_style= \"max-width:90%; height:auto;\" > and airspeed with the wind would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%2B30 ALIGN=MIDDLE  ALT=\"r%2B30\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  If the against the wind part of the trip takes t hours, then the return trip must take 10 - t hours, because the entire trip took 10 hours.\r<BR>\n" );
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document.write( "The formula for straight-line distance in terms of constant rate over a period of time is <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;\" >.  So we can express time as a function of distance and rate by saying <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=d%2Fr ALIGN=MIDDLE  ALT=\"t=d%2Fr\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "In our case, the time for the outbound trip, t, is given by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=720%2F%28r-30%29 ALIGN=MIDDLE  ALT=\"t=720%2F%28r-30%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  The time for the return trip, 10 - t, is given by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10-t=720%2F%28r%2B30%29 ALIGN=MIDDLE  ALT=\"10-t=720%2F%28r%2B30%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "First solve this second equation for t:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-t=%28720%2F%28r%2B30%29%29-10 ALIGN=MIDDLE  ALT=\"-t=%28720%2F%28r%2B30%29%29-10\"   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=t=10-%28720%2F%28r%2B30%29%29 ALIGN=MIDDLE  ALT=\"t=10-%28720%2F%28r%2B30%29%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=t=%2810%28r%2B30%29-720%29%2F%28r%2B30%29 ALIGN=MIDDLE  ALT=\"t=%2810%28r%2B30%29-720%29%2F%28r%2B30%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=t=%2810r%2B300-720%29%2F%28r%2B30%29 ALIGN=MIDDLE  ALT=\"t=%2810r%2B300-720%29%2F%28r%2B30%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=t=%2810r-420%29%2F%28r%2B30%29 ALIGN=MIDDLE  ALT=\"t=%2810r-420%29%2F%28r%2B30%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now, note that we have two expressions for t in terms of r.  Set them equal to each other:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=720%2F%28r-30%29=%2810r-420%29%2F%28r%2B30%29 ALIGN=MIDDLE  ALT=\"720%2F%28r-30%29=%2810r-420%29%2F%28r%2B30%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Multiply by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28r%2B30%29%28r-30%29 ALIGN=MIDDLE  ALT=\"%28r%2B30%29%28r-30%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=720%28r%2B30%29=%2810r-420%29%28r-30%29 ALIGN=MIDDLE  ALT=\"720%28r%2B30%29=%2810r-420%29%28r-30%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Distribute and collect terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=720r%2B21600=10r%5E2-300r-420r%2B12600 ALIGN=MIDDLE  ALT=\"720r%2B21600=10r%5E2-300r-420r%2B12600\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10r%5E2-1440r-9000=0 ALIGN=MIDDLE  ALT=\"10r%5E2-1440r-9000=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Divide by 10\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E2-144r-900=0 ALIGN=MIDDLE  ALT=\"r%5E2-144r-900=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Note that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-150%2A6=-900 ALIGN=MIDDLE  ALT=\"-150%2A6=-900\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-150%2B6=-144 ALIGN=MIDDLE  ALT=\"-150%2B6=-144\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28r-150%29%28r%2B6%29=0 ALIGN=MIDDLE  ALT=\"%28r-150%29%28r%2B6%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > => <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=150 ALIGN=MIDDLE  ALT=\"r=150\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=-6 ALIGN=MIDDLE  ALT=\"r=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The solution set to the quadratic is therefore 150 or -6.  Since flying backwards doesn't make much sense, exclude the -6 value as an extraneous root.  The speed in still air is 150 miles per hour.\r<BR>\n" );
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document.write( "Check:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=720%2F%28150-30%29=720%2F120=6 ALIGN=MIDDLE  ALT=\"720%2F%28150-30%29=720%2F120=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=720%2F%28150%2B30%29=720%2F180=4 ALIGN=MIDDLE  ALT=\"720%2F%28150%2B30%29=720%2F180=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and finally, 6 + 4 = 10.  Answer checks.\r<BR>\n" );
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document.write( "Hope that helps,<BR>\n" );
document.write( "John </SPAN>\n" );
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