Answer
The time required to reach maximum height is less than the time required for the ball to fall back down to its starting point.
Work Step by Step
$\sum F = ma$
$a = \frac{\sum F}{m}$
As the ball is going up, the force of gravity $mg$ and the force of air resistance $F_a$ are both directed toward the ground.
$a = \frac{\sum F}{m} = \frac{mg+F_a}{m}$
As the ball is going down, the force of gravity $mg$ is directed down but the force of air resistance $F_a$ is directed up.
$a = \frac{\sum F}{m} = \frac{mg-F_a}{m}$
The magnitude of acceleration is greater when the ball is moving upward. Therefore the ball will come to rest at maximum height in a shorter time than the ball takes to return to its starting point.
