document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=202504>Question 202504</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this word problem:<BR>\n" );
document.write( "An airplane can travel a distance of 6,000 km in 6 hours with the wind. The return trip against the wind takes 7.5 hours. The rate of the airplane in still air is<BR>\n" );
document.write( "a. 1,000 km/hr<BR>\n" );
document.write( "b. 994 km/hr<BR>\n" );
document.write( "c. 900 km/hr<BR>\n" );
document.write( "d. 800 km/hr </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #152727 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=152727\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> plane travels 6000 km in 6 hours with the wind.<BR>\n" );
document.write( "plane travels 6000 km in 7.5 hours against the wind.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "let p = speed of plane in still air.<BR>\n" );
document.write( "let w = speed of wind<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "total speed = plane speed plus or minus wind speed.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "let (p+w) = speed of plane with the wind.<BR>\n" );
document.write( "let (p-w) = speed of plane against the wind.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "rate * time = distance<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "with the wind:<BR>\n" );
document.write( "6 * (p+w) = 6000<BR>\n" );
document.write( "against the wind:<BR>\n" );
document.write( "7.5 * (p-w) = 6000<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "since they both = 6000, they equal each other, so:<BR>\n" );
document.write( "6*(p+w) = 7.5*(p-w)<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "this becomes:<BR>\n" );
document.write( "6*p + 6*w = 7.5*P - 7.5*w<BR>\n" );
document.write( "subtracting 6*p from both sides of this equation and adding 7.5*w to both sides of this equation gets:<BR>\n" );
document.write( "1.5*p = 13.5*w<BR>\n" );
document.write( "dividing both sides of this equation by 1.5 gets:<BR>\n" );
document.write( "p = 9*w<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "we can substitute 9*w for p in either equation.<BR>\n" );
document.write( "take with the wind.<BR>\n" );
document.write( "6*p + 6*w = 6000 becomes:<BR>\n" );
document.write( "6*9*w + 6*w = 6000 after substituting 9*w for p.<BR>\n" );
document.write( "this becomes:<BR>\n" );
document.write( "54*w + 6*w = 6000 which becomes:<BR>\n" );
document.write( "60*w = 6000<BR>\n" );
document.write( "w = 100<BR>\n" );
document.write( "substituting w = 100 in the second equation gets:<BR>\n" );
document.write( "7.5*p - 7.5*(100) = 6000<BR>\n" );
document.write( "adding 7.5*(100) to both sides of this equation gets:<BR>\n" );
document.write( "7.5*p = 6000 + 750 = 6750<BR>\n" );
document.write( "dividing both sides of this equation by 7.5 gets:<BR>\n" );
document.write( "p = 6750 / 7.5 = 900<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "we have:<BR>\n" );
document.write( "p = 900<BR>\n" );
document.write( "w = 100<BR>\n" );
document.write( "with the wind, the equation becomes:<BR>\n" );
document.write( "6 * (100+900) = 6 * 1000 = 6000 which checks out ok.<BR>\n" );
document.write( "against the wind, the equation becomes:<BR>\n" );
document.write( "7.5 * (900 - 100) = 7.5 * (800) = 6000 which checks out ok again.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "speed of the plane in still air is 900 kmph (kilometers per hour).<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );