document.write( "Question 474433: It took the pilot an hour and a half to make a flight of 240 miles when flying against a headwind. The return trip took an hour and twelve minutes (the wind had not shifted nor changed its speed). What was the spped of the wind?\r
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\n" ); document.write( "\n" ); document.write( "I have to solve this in Cramer's Rule and I know the process of solving it using that method, but my problem is that I don't or I'm confused on how to form the two equations needed. \n" ); document.write( "

Algebra.Com's Answer #325386 by Theo(13342) $\"\"$ $\"About$

You can put this solution on YOUR website!
rate * time = distance
\n" ); document.write( "r * t = d
\n" ); document.write( "d = 240 miles
\n" ); document.write( "t = 1.5 hours against the wind.
\n" ); document.write( "t too 1.2 hours with the wind.
\n" ); document.write( "the rate against the wind is p-w
\n" ); document.write( "the rate with the wind is p+w
\n" ); document.write( "the formula against the wind would be:
\n" ); document.write( "(p-w)*1.5 = 240
\n" ); document.write( "the formula with the wind would be:
\n" ); document.write( "(p+w)*1.2 = 240
\n" ); document.write( "solve these 2 equations simultaneously to get:
\n" ); document.write( "p = 180
\n" ); document.write( "w = 20
\n" ); document.write( "the system of equations that needs to be solved is:
\n" ); document.write( "(p-w)*1.5 = 240
\n" ); document.write( "and:
\n" ); document.write( "(p+w)*1.2 = 240
\n" ); document.write( "expand both these equations and you get:
\n" ); document.write( "1.5p - 1.5w = 240
\n" ); document.write( "1.2p + 1.2w = 240
\n" ); document.write( "you can solve these by substitution, elimination, matrix of coefficients, or any other applicable method including cramer's rule.
\n" ); document.write( "p is the equal to the speed of the plane (rate).
\n" ); document.write( "w is equal to the speed of the wind (rate).
\n" ); document.write( "when the plane is traveling with the wind, the combined rate is (p+w).
\n" ); document.write( "when the plane is traveling against the wind, the combined rate is (p-2).
\n" ); document.write( "in matrix form, this system would look like this:
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document.write( "  x       y        c     \r\n" );
document.write( "  1.5     -1.5     240\r\n" );
document.write( "  1.2     1.2      240\r\n" );
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\n" ); document.write( "using Cramer's Rule of Determinants, then:
\n" ); document.write( "x = Dx/D and y = Dy/D
\n" ); document.write( "D = (1.5*1.2) - (1.2*-1.5) which equals 3.6
\n" ); document.write( "Dx = (240*1.2)-(240*-1.5) which equals 648
\n" ); document.write( "Dy = (1.5*240)-(1.2*240) = 72
\n" ); document.write( "x = Dx/D = 648/3.6 = 180
\n" ); document.write( "y = Dy/D = 72/3.6 = 20
\n" ); document.write( "We get the same answer, as we should.
\n" ); document.write( "Here's a reference on Cramer's rule for Determinants in case you don't have it.
\n" ); document.write( "http://www.okc.cc.ok.us/maustin/Cramers_Rule/Cramer%27s%20Rule.htm
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