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?
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.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! rate * time = distance
r * t = d
d = 240 miles
t = 1.5 hours against the wind.
t too 1.2 hours with the wind.
the rate against the wind is p-w
the rate with the wind is p+w
the formula against the wind would be:
(p-w)*1.5 = 240
the formula with the wind would be:
(p+w)*1.2 = 240
solve these 2 equations simultaneously to get:
p = 180
w = 20
the system of equations that needs to be solved is:
(p-w)*1.5 = 240
and:
(p+w)*1.2 = 240
expand both these equations and you get:
1.5p - 1.5w = 240
1.2p + 1.2w = 240
you can solve these by substitution, elimination, matrix of coefficients, or any other applicable method including cramer's rule.
p is the equal to the speed of the plane (rate).
w is equal to the speed of the wind (rate).
when the plane is traveling with the wind, the combined rate is (p+w).
when the plane is traveling against the wind, the combined rate is (p-2).
in matrix form, this system would look like this:
x y c
1.5 -1.5 240
1.2 1.2 240
using Cramer's Rule of Determinants, then:
x = Dx/D and y = Dy/D
D = (1.5*1.2) - (1.2*-1.5) which equals 3.6
Dx = (240*1.2)-(240*-1.5) which equals 648
Dy = (1.5*240)-(1.2*240) = 72
x = Dx/D = 648/3.6 = 180
y = Dy/D = 72/3.6 = 20
We get the same answer, as we should.
Here's a reference on Cramer's rule for Determinants in case you don't have it.
http://www.okc.cc.ok.us/maustin/Cramers_Rule/Cramer%27s%20Rule.htm
|
|
|
