document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=199712>Question 199712</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An airplane flew for 4 hours against a head wind of 40 km/h. On the return flight the same wind was a tail wind, and the flight took 3 hours. Find the speed of the airplane 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 #150087 by </B><A HREF=/tutors/aboutme.mpl?userid=tutorvolunteer><B>tutorvolunteer(9)</B></A><img src=\"/images/stars/stars-05.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=tutorvolunteer><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=150087\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Since distance = speed x time,  time = speed/distance +or- wind speed/distance\r<BR>\n" );
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document.write( "(+or- depending on whether it is in the same direction as plane, in which case it would be +, or opposite direction and -)\r<BR>\n" );
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document.write( "time = (speed +or- wind speed)/distance\r<BR>\n" );
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document.write( "(abbreviations used:  time: t, speed in still air: s, wind speed: ws, distance: d)\r<BR>\n" );
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document.write( "Let's look at the first scenario: t = 4, ws = -40.  Therefore,  since t = (s - ws)/d, we get this equation:\r<BR>\n" );
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document.write( "4 = (s - 40)/d  ----) this has 2 variable, which means we will need a system of equations to solve it.\r<BR>\n" );
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document.write( "Let's look at the second part of the question to get the second equation.  Since t=(s+ws)/d,  we get this:\r<BR>\n" );
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document.write( "3 = (s + 40)/d\r<BR>\n" );
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document.write( "Now we have our two equations. We can use algebra to solve for s, the wind speed in still air.\r<BR>\n" );
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document.write( "4d = s-40 , so  d = (s-40)/4  using eq 1.   Also, 3d = s+40, so d = (s+40)/3  using eq. 2\r<BR>\n" );
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document.write( "Now we have 2 equations solving for d. Since distance stays the same, we can set these equal to each other to solve for the wind speed in still air:\r<BR>\n" );
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document.write( "(s-40)/4 = (s+40)/3 \r<BR>\n" );
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document.write( "3(s-40) = 4(s+40)\r<BR>\n" );
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document.write( "3s - 120 = 4s + 160\r<BR>\n" );
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document.write( "3s - 280 = 4s\r<BR>\n" );
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document.write( "Therefore, s = 280 km/h  (ignore -, since only asking for speed, not direction) </SPAN>\n" );
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