document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=41867>Question 41867</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0072549017/algebrahomeworkh></A><BR>\n" );
document.write( ": <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?\r<BR>\n" );
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document.write( "Thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #27046 by </B><A HREF=/tutors/aboutme.mpl?userid=fractalier><B>fractalier(6550)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=fractalier><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=fractalier><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=27046\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In problems like this, we always use distance = rate * time, or D = RT.<BR>\n" );
document.write( "Thus T = D/R.  Let R be the plane's speed in still air.<BR>\n" );
document.write( "Going against the wind, we have<BR>\n" );
document.write( "T1 = 720 / (R - 30) and<BR>\n" );
document.write( "T2 = 720 / (R + 30)<BR>\n" );
document.write( "But these two times add to 10 hours, so we have<BR>\n" );
document.write( "720 / (R - 30) + 720 / (R + 30) = 10<BR>\n" );
document.write( "Now multiply everything by (R+30)(R-30) to clear fractions...<BR>\n" );
document.write( "720(R+30) + 720(R-30) = 10(R+30)(R-30)<BR>\n" );
document.write( "Now solve for R...<BR>\n" );
document.write( "720R + 21600 + 720R - 21600 = 10(R^2 - 900)<BR>\n" );
document.write( "1440R = 10(R^2 - 900)<BR>\n" );
document.write( "144R = R^2 - 900<BR>\n" );
document.write( "R^2 - 144R - 900 = 0<BR>\n" );
document.write( "(R - 150)(R + 6) = 0<BR>\n" );
document.write( "R = 150 mph </SPAN>\n" );
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