The packing process at a vaccine manufacturer produces vaccine vials in batches of $400$ units. The automated process can be broken down into the following steps.

$1.$ The packing machine is first filled up with liquid medicine. This step takes $10$ minutes.

$2.$ The machine then fills up empty vials one by one. This process takes $15$ seconds per vial.

$3.$ Once the entire batch of $400$ vials has been filled up$,$ the machine discards any leftover medicine and cleans itself to avoid any contamination. This step takes an additional $10$ minutes.

Assume that this sequence of steps is repeated forever and there is always sufficient supply of medicine and empty vials. What is the capacity of the packing process in vials$/$hr$?$ If your answer is not an integer, provide at least three decimal places, e$.$g$.,7\mathrm{.}500.$