Answer
The bird's air speed is 2.25mi/h and the windspeed is 0.75 mi/h.
Work Step by Step
The first step is to set up the equations.
X= Bird's airspeed and Y= wind speed.
Airspeed + wind speed = ground speed with the tailwind
$x+y=3$
Airspeed - wind speed = ground speed with the headwind
$x-y=1.5$
Upon inspection, it is clear that these equations can be added together to eliminate the y variable.
$2x=4.5$ is the resulting equation because the y variable is eliminated and $3 + 1.5 = 4.5 $.
Dividing both sides of the equation by 2 results in $x=2.25$.
We can substitute this value back into the first equation to get the y value.
$2.25+y=3$. Solving for this would give us $y=0.75$.
We now know both variables: $x=2.25$ and $y=0.75$.
