Final answer:
The time required to roast a turkey remains four hours, regardless of whether three or four people are involved, because the task's time is fixed and not influenced by the number of people.
Step-by-step explanation:
The student's question pertains to a scenario in which time required to perform a task does not necessarily decrease proportionally with an increase in people, because of the fixed size of the task.
In the given example of roasting a turkey, the number of people does not change the time it takes to roast the turkey because roasting a turkey is generally a task that takes a set amount of time regardless of how many people are involved.
Therefore, the time it takes to roast the turkey remains the same, which is four hours, whether there are three or four people involved. This concept is similar to what's described in the reference information involving economics of scale and productivity, but in this particular question, productivity doesn't increase since the capacity of the task (roasting the turkey) cannot be increased.
To determine how many hours it would take four people to roast the same turkey, we can use the concept of work done. If it took three people four hours to roast the turkey, they collectively did 3 x 4 = 12 hours of work. Now, let's assume each person works at the same rate.
If four people work together, they would need to do a total of 12 hours of work. Since each person works at the same rate, it would take the four people 12 hours in total to roast the turkey.