Solve the Problem $h = - 16 t ^ { 2 } + 600$

Multiple Choice

Solve the problem.
-A person at the top of a 600 foot tall building drops a yellow ball. The height of the yellow ball is given by the equation $h = - 16 t ^ { 2 } + 600$ where $h$ is measured in feet and $t$ is the number of seconds since the yellow ball was dropped. A second person, in the same building but on a lower floor that is 408 feet from the ground, drops a white ball 3 seconds after the yellow ball was dropped. The height of the white ball is given by the equation $\mathrm { h } = - 16 ( \mathrm { t } - 3 ) ^ { 2 } + 408$ where $\mathrm { h }$ is measured in feet and $\mathrm { t }$ is the number of seconds since the yellow ball was dropped. Find the time that the balls are the same distance above the ground and find this distance.

A) $3.5$ seconds; 404 feet
B) $2.5$ seconds; 500 feet
C) 3 seconds; 456 feet
D) 4 seconds; 344 feet