The setup time in a sequential batch production operation is $2\mathrm{.}0$ hours, and the actual processing time of $1\mathrm{.}60$min per cycle. Three parts are produced each cycle. No tool handling time is included in the cycle. Part handling time each cycle is $45sec.$ It consists of the worker obtaining two starting work units from a parts tray, loading them into the machine, and then after processing, unloading the completed parts and placing them into the same tray. Each tray holds $24$ parts. When all of the starting work units have been replaced with completed parts, the tray of completed parts is moved aside and a new tray of starting units is moved into position at the machine. This irregular work element takes $4\mathrm{.}0$min. Batch quantity is $2400$ units. The average cycle time is$?$ The time to complete the batch? The average production rate is how many pieces per hour?