document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=558130>Question 558130</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A passenger plane flew to moscow and back. The trip there took five hours and the trip back took nine hours.  It averaged 144 km/h faster on the trip there than on the return trip.  Find the passenger plane's average speed on the outbound trip.\r<BR>\n" );
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document.write( "O.k so I did have a go at it Trying to use a system of equations using the substitution method to eliminate one unknown but it didn't work.  I will try and explain what I was playing around with:\r<BR>\n" );
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document.write( "D1 = Distance there  D2 = Distance back ( but not sure if I needed this as it is same Distance )<BR>\n" );
document.write( "Average Speed = S  \r<BR>\n" );
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document.write( "D1/5 + D2/9 = S\r<BR>\n" );
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document.write( "D1/5 = D2/9+144 ( I tried substituting this in )\r<BR>\n" );
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document.write( "D2/9+144 + D2/9 = S ( then I combined the like terms )\r<BR>\n" );
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document.write( "D2/18+144 = s ( but this is where I realized I had failed as I still had 2 variables.\r<BR>\n" );
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document.write( "Please help me someone I am so bad at word problems and I would love to be confident at them. \r<BR>\n" );
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document.write( "P.S I wasn't sure about which was the outbound trip, I guessed it meant the trip back.\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #362920 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=362920\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the answer is:<BR>\n" );
document.write( "plane speed equals 252 kmph<BR>\n" );
document.write( "wind speed equals 72 kmph<BR>\n" );
document.write( "distance equals 1620 km<BR>\n" );
document.write( "the basic formula is rate * time = distance<BR>\n" );
document.write( "let p = speed of the plane and let w = speed of the wind.<BR>\n" );
document.write( "going there the formula becomes:<BR>\n" );
document.write( "(p+w)*5 = d<BR>\n" );
document.write( "coming back the formula becomes:<BR>\n" );
document.write( "(p-w)*9 = d<BR>\n" );
document.write( "since they're both equal to d (the distance is the same going and coming), you can set them equal to each other to get:<BR>\n" );
document.write( "(p+w)*5 = (p-w)*9<BR>\n" );
document.write( "simplify this equation to get:<BR>\n" );
document.write( "5p + 5w = 9p - 9w<BR>\n" );
document.write( "subtract 5p from both sides of this equation and add 9w to both sides of this equation to get:<BR>\n" );
document.write( "14w = 4p<BR>\n" );
document.write( "solve for p to get:<BR>\n" );
document.write( "p = 14w/4<BR>\n" );
document.write( "they are also telling you that the plane averaged 144 km/h faster on the trip there than on the return trip.<BR>\n" );
document.write( "this means that:<BR>\n" );
document.write( "they are talking about the speed of the plan going versus the speed of the plane coming back which is the rate part of the rate * time = distance equation.<BR>\n" );
document.write( "this means that:<BR>\n" );
document.write( "p + w = p - w + 144<BR>\n" );
document.write( "the speed of the plane going is p + w<BR>\n" );
document.write( "the speed of the plane coming back is p - w<BR>\n" );
document.write( "subtract p from both sides of that equation and add w to both sides of that equation to get:<BR>\n" );
document.write( "2w = 144<BR>\n" );
document.write( "divide both sides of that equation by 2 to get:<BR>\n" );
document.write( "w = 72<BR>\n" );
document.write( "that's the speed of the wind.<BR>\n" );
document.write( "now that you know the speed of the wind, you can go back to the equation of:<BR>\n" );
document.write( "p = 14w/4 to get:<BR>\n" );
document.write( "p = (14*72)/4 which becomes:<BR>\n" );
document.write( "p = 252<BR>\n" );
document.write( "the speed of the plane in still air is 252 km/h<BR>\n" );
document.write( "the speed of the wind is 72 km/h<BR>\n" );
document.write( "going, the formula of:<BR>\n" );
document.write( "(p+w)*5 = d becomes:<BR>\n" );
document.write( "(252+72)*5 = d which becomes:<BR>\n" );
document.write( "d = 1620 km.<BR>\n" );
document.write( "coming back, the formula of:<BR>\n" );
document.write( "(p-w)*9 = d becomes:<BR>\n" );
document.write( "(252-72)*9 = d which becomes:<BR>\n" );
document.write( "d = 1620 km.<BR>\n" );
document.write( "d is the same in both directions as it should be.<BR>\n" );
document.write( "the answer is:<BR>\n" );
document.write( "plane speed is 252 kmph<BR>\n" );
document.write( "wind speed is 72 kmph<BR>\n" );
document.write( "the passenger plane's average speed going is 252+72 = 324 kmph<BR>\n" );
document.write( "the passenger plane's average coming back is 252-72 = 180 kmph<BR>\n" );
document.write( "that's the net speed when you take the speed of the wind into account.<BR>\n" );
document.write( "outbound depends on where you're looking from.<BR>\n" );
document.write( "if you're looking from where you started from, then outbound would be going to moscow.<BR>\n" );
document.write( "if you're looking from moscow, then outbound would be coming back.<BR>\n" );
document.write( "i suspect they mean going to moscow but can't be sure the way it's worded.<BR>\n" );
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