The system stores all time values as the decimal part of a day. The format you to display this data doesn't change this fact. You may think the cell contains 8AM but if you select the cell and change the format to General, you will see the actual value 0.333333. (Even that is not the actual contents., The system stores number as floating point values in binary.)
So leave the format for the start time, end time, and duration as a convenient time format for ease of reading. In the cell where you sum the durations, change the format to General or Number with an appropriate number of decimal places. This will yield the number of 24-hour days worked. Then simply multiply by 24 to get the hours worked and divide by the number of work hours in a day to get the number of days you should be paid for.
This is my sample: