An archivist uses a radiation detector to assess a vintage pocket watch with radium-painted hands.

To determine the radiation emitted solely by the watch, the archivist performs two measurements:

1. They measure the background radiation in the empty archive room, recording $216$ counts over a duration of $12minutes$.
2. They place the watch close to the detector and record $3408$ counts over a period of $4minutes$.

Calculate the corrected count rate of the pocket watch in counts per second.