document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=885699>Question 885699</A>: <I><SPAN STYLE=\"word-break: break-all;\"> At what air speed must a plane be flown to complete a trip between two airports 420 miles apart in 5 hours if the flight going has a head wind (blowing against the nose of the plane) of 40 mph and the flight returning has a tail wind of 30 mph? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #535431 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=535431\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> At what air speed must a plane be flown to complete a trip between two airports 420 miles apart in 5 hours if the flight going has a head wind (blowing against the nose of the plane) of 40 mph and the flight returning has a tail wind of 30 mph?<BR>\n" );
document.write( ":<BR>\n" );
document.write( "let s = air speed required for this scenario<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(s-40) = ground speed against the wind<BR>\n" );
document.write( "and<BR>\n" );
document.write( "(s+30) = ground speed with the wind<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Write a time equation; time = dist/speed<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=420%2F%28%28s-4%29%29%29 ALIGN=MIDDLE  ALT=\"420%2F%28%28s-4%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=420%2F%28%28s%2B30%29%29 ALIGN=MIDDLE  ALT=\"420%2F%28%28s%2B30%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 5<BR>\n" );
document.write( "multiply by (s-40)(s+30)<BR>\n" );
document.write( "(s-40)(s+30)*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=420%2F%28%28s-40%29%29%29 ALIGN=MIDDLE  ALT=\"420%2F%28%28s-40%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + (s-40)(s+30)*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=420%2F%28%28s%2B30%29%29 ALIGN=MIDDLE  ALT=\"420%2F%28%28s%2B30%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 5(s-40)(s+30)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Cancel the denominators, FOIL the right side, resulting in:<BR>\n" );
document.write( "420(s+30) + 420(s-40) 5(s^2+30s-40s-1200)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "420s + 12600 + 420s - 16800 5(s^2 - 10s - 1200)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "840s - 4200 = 5s^2 - 50s - 6000<BR>\n" );
document.write( "0 = 5s^2 - 50s - 840s - 6000 + 4200<BR>\n" );
document.write( "0 = 5s^2 - 890s - 1800<BR>\n" );
document.write( "simplify divide by 5<BR>\n" );
document.write( "s^2 - 178s - 360 = 0<BR>\n" );
document.write( "You can us the quadratic formula here but this will factor to<BR>\n" );
document.write( "(s-180) (s+2) = 0<BR>\n" );
document.write( "the positive solution<BR>\n" );
document.write( "s = 180 mph is the air speed of the aircraft<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Check this by finding the flight time for each way<BR>\n" );
document.write( "420/140 = 3 hr (40 mph head wind)<BR>\n" );
document.write( "420/210 = 2 hr (30 mph tail wind)<BR>\n" );
document.write( "------------------<BR>\n" );
document.write( "total time 5 hrs<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );