Answer:
Step-by-step :
a) To find the constant proportionality, we can use the formula:
Number of applications = k * (number of workers) * (number of hours)
where k is the constant proportionality we want to find. We can plug in the values given in the problem:
466 = k * 8 * 12
Solving for k:
k = 466 / (8 * 12) = 4.875
So the formula is:
Number of applications = 4.875 * (number of workers) * (number of hours)
b) If 3 workers are sick, then 8 - 3 = 5 workers are left. To find how long they will have to work to assemble 466 applications, we can again use the formula:
466 = 4.875 * 5 * (number of hours)
Solving for the number of hours:
number of hours = 466 / (4.875 * 5) = 19.07 hours (rounded to two decimal places)
So the remaining workers will have to work for approximately 19.07 hours to assemble 466 applications.
c) If the task has to be accomplished in 4 hours, we can again use the formula with the new values:
466 = 4.875 * (number of workers) * 4
Solving for the number of workers:
number of workers = 466 / (4.875 * 4) = 23.97
Since we cannot have a fraction of a worker, we need to round up to the nearest whole number of workers.
Therefore, we would need to hire 24 temporary workers to accomplish the task in 4 hours.