document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=620145>Question 620145</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello, I need help in solving this problem:\r<BR>\n" );
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document.write( "A plane flew 150 kilometers with a 30 km/hr tailwind, then turned into the wind<BR>\n" );
document.write( "and flew for another 65 kilometers. If the wind and the plane’s airspeed were<BR>\n" );
document.write( "constant and the entire trip took 30 minutes, what was the plane’s airspeed?<BR>\n" );
document.write( "(Ignore the time needed to turn the plane around).\r<BR>\n" );
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document.write( "Thank you. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #389944 by </B><A HREF=/tutors/aboutme.mpl?userid=htmentor><B>htmentor(1343)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=htmentor><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=htmentor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=389944\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let s = the plane's airspeed<BR>\n" );
document.write( "The total time of the trip is 30 mins = 1/2 hr; the speed of the wind = 30 km/hr<BR>\n" );
document.write( "Since t = d/v, we can write the following for the total time of the trip:<BR>\n" );
document.write( "150/(s+30) + 65/(s-30) = 0.5<BR>\n" );
document.write( "Combine fractions using the common denominator, and cross-multiply:<BR>\n" );
document.write( "150(s-30) + 65(s+30) = 0.5(s^2-900)<BR>\n" );
document.write( "Simplify and collect terms:<BR>\n" );
document.write( "s^2 - 430s + 4200 = 0<BR>\n" );
document.write( "This can be factored as<BR>\n" );
document.write( "(s-10)(s-420) = 0<BR>\n" );
document.write( "The solutions are s = 10, s = 420<BR>\n" );
document.write( "Since the speed of the plane cannot be less than the wind speed, we take the 2nd solution.<BR>\n" );
document.write( "So s = 420 km/hr<BR>\n" );
document.write( "Check:<BR>\n" );
document.write( "150/450 + 65/390 = 1/3 + 1/6 = 3/6 = 1/2<BR>\n" );
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