document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=165150>Question 165150</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0618609539/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> a plane flying with the tail wind flew 600 miles in 5hrs. Against the wind, the plane requires 6 hours to fly the same distance. Find the rate of the plane in the calm air and the rate 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 #121725 by </B><A HREF=/tutors/aboutme.mpl?userid=ptaylor><B>ptaylor(2198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ptaylor><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=ptaylor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=121725\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Distance(d) equals Rate(r) times Time(t) or d=rt; r=d/t and t=d/r\r<BR>\n" );
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document.write( "Let r=rate of plane in calm air <BR>\n" );
document.write( "And let w=rate of the wind\r<BR>\n" );
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document.write( "Now we are told the following: (t=d/r)<BR>\n" );
document.write( "5=600/(r+w)  Multiply each term by (r+w)<BR>\n" );
document.write( "5(r+w)=600 get rid of parens (distributive law)<BR>\n" );
document.write( "5r+5w=600 divide each term by 5<BR>\n" );
document.write( "r+w=120------------------------------------------------eq1<BR>\n" );
document.write( "and<BR>\n" );
document.write( "6=600/(r-w)Multiply each term by (r-w)<BR>\n" );
document.write( "6(r-w)=600 get rid of parens<BR>\n" );
document.write( "6r-6w=600 divide each term by 6<BR>\n" );
document.write( "r-w=100-------------------------------------eq2\r<BR>\n" );
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document.write( "(NOTE: WHEN TRAVELLING WITH THE WIND, WE HAVE TO ADD THE WIND SPEED AND AGAINST THE WIND, WE SUBTRACT THE WIND SPEED)\r<BR>\n" );
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document.write( "Next, add eq1 and eq2 and we get:<BR>\n" );
document.write( "2r=220  divide each side by 2<BR>\n" );
document.write( "r=110 mph --------------------------rate of plane in calm air<BR>\n" );
document.write( "substitute r=110 into eq1<BR>\n" );
document.write( "110+w=120 subtract 110 from each side<BR>\n" );
document.write( "110-110+w=120-110  collect like terms<BR>\n" );
document.write( "w=10 mph-----------------------------------rate of the wind<BR>\n" );
document.write( "CK<BR>\n" );
document.write( "5=600/(110+10)<BR>\n" );
document.write( "5=600/120<BR>\n" );
document.write( "5=5<BR>\n" );
document.write( "and<BR>\n" );
document.write( "6=600/(110-10)<BR>\n" );
document.write( "6=600/100<BR>\n" );
document.write( "6=6\r<BR>\n" );
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document.write( "Hope this helps----ptaylor<BR>\n" );
document.write( " </SPAN>\n" );
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