document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=78762>Question 78762</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Speed of an airplane in still air is 255 km/h. plane travels 675km against wind and 1449 km with the wind in a total of 10 hr. What is the speed of the wind?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #56523 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=56523\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Speed of an airplane in still air is 255 km/h. Plane travels 675 km against wind and 1449 km with the wind in a total of 10 hr. What is the speed of the wind?<BR>\n" );
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document.write( "Let x = speed of the wind<BR>\n" );
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document.write( "Speed with the wind = (255+x)<BR>\n" );
document.write( "Speed against the wind = (255-x)<BR>\n" );
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document.write( "Time = dist/speed<BR>\n" );
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document.write( "Time against the wind + Time with the wind = 10 hrs<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=675%2F%28%28255-x%29%29 ALIGN=MIDDLE  ALT=\"675%2F%28%28255-x%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1449%2F%28%28255%2Bx%29%29 ALIGN=MIDDLE  ALT=\"1449%2F%28%28255%2Bx%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 10<BR>\n" );
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document.write( "Multiply equation by (255-x)(255+x) and you have:<BR>\n" );
document.write( "675(255+x) + 1449(255-x) = 10(255+x)(255-x)<BR>\n" );
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document.write( "172125 + 675x + 369495 - 1449x = 10(65025 - x^2)<BR>\n" );
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document.write( "541620 - 774x = 650250 - 10x^2 <BR>\n" );
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document.write( "10x^2 - 774x + 541620 - 650250 = 0; all terms on the left<BR>\n" );
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document.write( "10x^2 - 774x - 108630 = 0: a quadratic equation<BR>\n" );
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document.write( "Simplify, divide equation by 2:<BR>\n" );
document.write( "5x^2 - 387x - 54315 = 0<BR>\n" );
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document.write( "Use the quadratic formula: a=5, b=-387, c=-54315<BR>\n" );
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document.write( "The positive solution: x = 149.47, call it 149.5 mph is the wind speed<BR>\n" );
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document.write( "Check on a calculator the times with and against the wind:<BR>\n" );
document.write( "675/(255-149.5) = 6.4 hrs<BR>\n" );
document.write( "1489/(255+149.5)= 3.7 hrs<BR>\n" );
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document.write( "Total times = 10.1 ~ 10 hrs as given   </SPAN>\n" );
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