Acceleration problem

A person is on the roof of a building, 46.0 m above the ground. His teacher, who is 1.80 meters tall, is walking toward the building at a constant speed of 1.20 m/s. If the person wishes to drop the egg on his teacher's head, where should the teacher be when the person releases the egg?

So I know that I need to set two equations equal to each other to get the position the teacher needs to be for the egg to drop on him. So should I use $x = v_{y}_{0}t + \frac{1}{2} a_{x}t^{2}$ for the egg, and $x = x_{0} + v_{x}_{0}t + \frac{1}{2} a_{x}t^{2}$?

Thanks

1. $46 - 1.8 = 44.2 m$
2. $44.2 = \frac{1}{2} (9.8) t^{2}, t = 3$
3. $x = 0 + 1.20(3) = 3.6 m$