A tank holds 60 liters and fills at 4 liters per minute. How long does it take to fill an empty tank?
The problem asks for the time required to fill an empty tank with a total capacity of \(60\) liters, given a constant filling rate of \(4\) liters per minute. We are given the following data:
Our objective is to determine the time (\(t\)) required to fill the tank from \(0\) liters to \(60\) liters. Since the filling rate is constant, the relationship between volume, rate, and time is given by the formula:
\[V = r \times t\]
To find the time required, we rearrange the formula \(V = r \times t\) to solve for \(t\):
\[t = \frac{V}{r}\]
Substituting the given values, \(V = 60\) liters and \(r = 4\) liters per minute, we get:
\[t = \frac{60}{4}\]
Performing the division:
\[t = 15\]
Therefore, it takes \(15\) minutes to fill the tank. Comparing this with the given options, this result matches option B.
This problem demonstrates the concept of a constant rate, which is common in many real-life situations. For instance, if you are filling a swimming pool with a garden hose or adding fuel to a car, you can estimate how long the process will take by dividing the total capacity by the flow rate. By knowing the rate of flow (e.g., in liters per minute or gallons per minute), you can efficiently manage your time and resources for various tasks involving filling, emptying, or transferring fluids.