Matt and Anna are frequent fliers on Fast n Go Airplanes. They often fly between two cities that are a distance of 1680 miles apart. On one particular trip, they flew into the wind and the trip took 4 hours. the return trip with the wind behind them, only took about 3 hours. Find the speed of the wind and the speed of the plane in still air .
The Wind Speed is ____ mph
The Speed of the Plane is ____ mph
Also,
-3x - y = 4
y - 4z = 10
x - 4y + z = -12
What is (X, Y, Z)
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Matt n Anna are frequent fliers om fast n go airlines. They often fly between two cities that are 1545 miles apart. On one particular trip they flew into wind and trip took 4.5 hours The return trip with wind behind them trip only took 3.5 hours. Find the speed of the wind and speed of place in still air
To find the speed of the wind and the speed of the plane in still air, we can use some basic algebraic techniques.
Let's start by defining the variables:
Let p be the speed of the plane in still air.
Let w be the speed of the wind.
On the trip into the wind, the effective speed of the plane would be p - w. The distance traveled is 1680 miles and the time taken is 4 hours. Therefore, we can set up the equation:
Distance = Speed × Time
1680 = (p - w) × 4
On the return trip with the wind, the effective speed of the plane would be p + w. The distance is still 1680 miles, but the time taken is 3 hours. Setting up the equation:
1680 = (p + w) × 3
Now we have a system of equations. We can solve it using the method of substitution or elimination.
Let's use the method of substitution to solve. From the first equation, we can isolate p:
p - w = 1680/4
p - w = 420
p = 420 + w
Now substitute this value of p into the second equation:
1680 = (420 + w + w) × 3
1680 = (420 + 2w) × 3
1680 = 1260 + 6w
6w = 1680 - 1260
6w = 420
w = 420/6
w = 70
The speed of the wind is 70 mph.
Now substitute the value of w into p = 420 + w:
p = 420 + 70
p = 490
The speed of the plane in still air is 490 mph.
Now, let's move on to the system of equations:
-3x - y = 4
y - 4z = 10
x - 4y + z = -12
We can solve this system of equations using various methods such as substitution, elimination, or matrix methods. Let's use the method of elimination:
Multiply the first equation by -1:
3x + y = -4
Now add the first equation to the second equation:
(3x + y) + (y - 4z) = -4 + 10
3x + 2y - 4z = 6
Now add the second equation to the third equation:
(y - 4z) + (x - 4y + z) = 10 + (-12)
x - 3y - 3z = -2
So, the system of equations becomes:
3x + 2y - 4z = 6
x - 3y - 3z = -2
We can now solve this system of equations using a method of our choice, such as substitution or elimination.