With a tailwind, a bird flew at a ground speed of 3 mi/hr. Flying the same path against the same wind, the bird travels at a ground speed of 1.5 mi/hr. What is the bird's air speed? What is the wind speed?
W= wind speed
B= bird speed
B+W=3
B-W=1.5
add the equation
2B=4.5 Solve for B, then solve for W
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To find the bird's air speed and the wind speed, we can set up a system of equations.
Let's say the bird's air speed is represented by "x" and the wind speed is represented by "y".
When the bird is flying with a tailwind, the bird's ground speed is the sum of its air speed and the wind speed. In this case, the bird's ground speed is 3 mi/hr. So, we can write the equation:
x + y = 3 ----(1)
Similarly, when the bird is flying against the wind, its ground speed is the difference between its air speed and the wind speed. In this case, the bird's ground speed is 1.5 mi/hr. So, we can write the equation:
x - y = 1.5 ----(2)
Now, we have a system of equations:
x + y = 3 ----(1)
x - y = 1.5 ----(2)
To solve this system of equations, we can use the method of elimination:
Adding equation (1) and equation (2), we eliminate the variable "y" and solve for "x":
(x + y) + (x - y) = 3 + 1.5
2x = 4.5
x = 2.25
Putting the value of "x" back into equation (1), we can solve for "y":
2.25 + y = 3
y = 3 - 2.25
y = 0.75
Therefore, the bird's air speed is 2.25 mi/hr and the wind speed is 0.75 mi/hr.