Person-hours do not take account of the breaks that human beings generally require from work, e.g. for rest, eating and other bodily functions. They only count pure labour. Managers count the person-hours and add break time to estimate the amount of time a task will actually take to complete. Thus, while one college course's written paper might require twenty person-hours to carry out, it almost certainly will not get done in twenty consecutive hours. Its progress will be interrupted by work for other courses, meals, sleep and other distractions. (The exception to this rule is "cramming," when a student will attempt to do all of the work required for a project or an exam in one uninterrupted span of time.)
This is, of course, a naïve calculation that is only appropriate to certain types of activity. It is of most use when considering 'piece-work', where the activity being managed consists of discrete activities having simple dependencies, and where other factors can be neglected. So, adding another person to a packaging team will increase the output of that team in a predictable manner. In transport industry, this concept is superseded by passenger-kilometre and tonne-kilometre for better costing accuracy.
In reality, other factors intervene to reduce the simplicity of this model. If some elements of the task have a natural timespan, adding more staff will have a reduced effect: although having two chefs will double the speed of some elements of food preparation, they roast a chicken no faster than one chef. Some tasks also have a natural number of staff associated with them: the time to chop the vegetables will be halved with the addition of the second chef, but the time to carve the chicken will remain the same.
Another problem with this model, as Fred Brooks noted, is that organisation, training and co-ordination activities could more than outweigh the potential benefits of having extra staff working on a task.