Answer
Speed of bird with respect to the wind = Bird's air speed = 2.25 mi/h
Speed of the wind with respect to the ground = Wind's speed = 0.75 mi/h
Step-by-step explanation
Relative speed is usually given in terms of speed of a body A with respect to another body B (Vab)
Vab = Va - Vb
Vab = Speed of A relative to B
Va = Speed of A
Vb = Speed of B
So, for this question, when the bird is travelling in the same direction of wind, the speed of the bird with respect to the ground is 3 mi/h
(Speed of bird with respect to the wind)
= (Speed of bird with respect to ground) - (Speed of wind with respect to the ground)
Speed of bird with respect to the wind = x
Speed of bird with respect to ground = 3 mi/h
Speed of the wind with respect to the ground = y
(Speed of bird with respect to the wind)
= (Speed of bird with respect to ground) - (Speed of wind with respect to the ground)
x = 3 - y
When the bird is travelling in the opposite direction, the speed of the bird with respect to the ground is 1.5 mi/h
Speed of bird with respect to the wind = x
Speed of bird with respect to ground = 1.5 mi/h
Speed of the wind with respect to the ground = -y (Negative since the wind is in the opposite direction)
(Speed of bird with respect to the wind)
= (Speed of bird with respect to ground) - (Speed of wind with respect to the ground)
x = 1.5 - (-y)
x = 1.5 + y
We can the solve this system of equations
x = 3 - y
x = 1.5 + y
1.5 + y = 3 - y
y + y = 3 - 1.5
2y = 1.5
Divide both sides by 2
(2y/2) = (1.5/2)
y = 0.75 mi/h
x = 1.5 + y
x = 1.5 + 0.75
x = 2.25 mi/h
Hope this Helps!!!