document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=885722>Question 885722</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A plane goes 150 miles with the wind and returns against the wind in 3 hours and 45 minutes. Find the air speed of the plane if the wind blows 10 mph.\r<BR>\n" );
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document.write( "I tried to set it up as (150) / (s+10) + (150) / (s-10) = 3.75 but whenever I solve I don't get the right answer. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #535381 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=535381\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> RT=D for rate, time, distance.\r<BR>\n" );
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document.write( "10 mph = the speed of just the wind<BR>\n" );
document.write( "Let r = the speed of the plane if no wind\r<BR>\n" );
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document.write( "DATA TABLE often helps to think clearly about all the values and numbers used in the problem description.\r<BR>\n" );
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document.write( "______________________speed_________time_________distance<BR>\n" );
document.write( "WITH WIND_____________r+10__________(____)_______150<BR>\n" );
document.write( "AGAINST Wind__________r-10_________(_____)_______150<BR>\n" );
document.write( "TOTAL_______________________________3.75\r<BR>\n" );
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document.write( "You need expressions for times.  RT=D means you can divide left and right members of such an equation by R, so you have T=D/R.   Use this to fill the time slots in the table.\r<BR>\n" );
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document.write( "______________________speed_________time_________distance<BR>\n" );
document.write( "WITH WIND_____________r+10__________<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=150%2F%28r%2B10%29 ALIGN=MIDDLE  ALT=\"150%2F%28r%2B10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >_______150<BR>\n" );
document.write( "AGAINST Wind__________r-10_________<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=150%2F%28r-10%29 ALIGN=MIDDLE  ALT=\"150%2F%28r-10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >_______150<BR>\n" );
document.write( "TOTAL_______________________________3.75\r<BR>\n" );
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document.write( "The time column including the total gives you an equation in the variable, r:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28150%2F%28r%2B10%29%2B150%2F%28r-10%29=3.75%29 ALIGN=MIDDLE  ALT=\"highlight%28150%2F%28r%2B10%29%2B150%2F%28r-10%29=3.75%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "That is a large part of this solution process:  That analysis and obtaining the outlined equation.<BR>\n" );
document.write( "Solve the equation for r.\r<BR>\n" );
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document.write( "(I used r, while you used s.  I hope you are not bothered by that.)<BR>\n" );
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document.write( "(Now I see you got the same equation as I did, but you could not get an answer you were comfortable with.  Did you try multiplying left and right sides by (r+10)(r-10) and then simplify?)\r<BR>\n" );
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document.write( "Excuse me for skipping several steps; but you could get to <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3.75%5Er%5E2-300r-375=0 ALIGN=MIDDLE  ALT=\"3.75%5Er%5E2-300r-375=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and since the mixed decimal involves a denominator of 4, you can multiply left and right members by 4, yielding<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15r%5E2-1200r-1500=0 ALIGN=MIDDLE  ALT=\"15r%5E2-1200r-1500=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and continue to simplify this\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28highlight%28r%5E2-80r-100=0%29%29 ALIGN=MIDDLE  ALT=\"highlight%28highlight%28r%5E2-80r-100=0%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---- Now, solve THAT for r.<BR>\n" );
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document.write( "Use the general solution of a quadratic formula and simplify your expression.  I found <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28r=50%2B10sqrt%2817%29%29 ALIGN=MIDDLE  ALT=\"highlight%28r=50%2B10sqrt%2817%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
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