Final answer:
It would take 3 gardeners 10 hours to complete the task of landscaping the garden, as the time taken is inversely proportional to the number of gardeners.
Step-by-step explanation:
The time taken to landscape a garden is inversely proportional to the number of gardeners working on it. This means that if we increase the number of gardeners, the time taken decreases, and vice versa. The relationship can be described by the formula t = k/n, where t is the time taken, n is the number of gardeners, and k is the constant of proportionality.
From the information given, when 5 gardeners work, it takes 6 hours to complete the task. Thus, the constant k can be calculated as k = n × t, which gives us k = 5 × 6 = 30.
Now, to find how long it would take 3 gardeners to do the task, we rearrange the formula to t = k/n and substitute k = 30 and n = 3, which gives us t = 30/3 = 10 hours. Therefore, it would take 3 gardeners 10 hours to landscape the garden.