Final answer:
To determine the time it would take for seven groundskeepers to prepare a golf course, we set up a proportion based on the time taken by five groundskeepers (28 hours) and solved for the unknown time, yielding approximately 39.2 hours for seven groundskeepers.
Step-by-step explanation:
The question requests to calculate the time it would take for seven groundskeepers to prepare a golf course if five groundskeepers can complete the task in 28 hours. To solve this problem, we can apply the concept of directly proportional relationships because the amount of work done is directly proportional to the number of workers and the time they work.
When five groundskeepers take 28 hours, we assume that they provide a certain combined workload, which we can call 'work units'. If one groundskeeper works for 28 hours, it would yield 5 * 28 = 140 work units (since each groundskeeper would contribute 28 work units).
If we have seven groundskeepers, they would produce more 'work units' per hour. To find out how much time, t, it would take for seven groundskeepers to complete the same number of work units, we set up the proportion:
5 groundskeepers / 28 hours = 7 groundskeepers / t hours
Solving for t gives us:
5/28 = 7/t
5t = 7 * 28
t = (7 * 28) / 5
t = 196 / 5
t = 39.2 hours
Therefore, it would take seven groundskeepers approximately 39.2 hours to prepare the golf course.