Calculating Tank Filling Time A Step-by-Step Guide
In this article, we will delve into a practical problem involving fluid flow and time calculation. Specifically, we'll tackle the question: If 90 gallons of oil flow through a certain pipe in 18 minutes, how long will it take to fill a 600-gallon tank using this pipe? This is a classic problem that combines basic arithmetic with real-world applications. Understanding how to solve such problems is crucial for various fields, including engineering, physics, and even everyday situations like filling a swimming pool or a water tank. We will break down the problem step by step, ensuring clarity and comprehension for readers of all backgrounds. The goal is not just to provide the answer but also to explain the underlying principles and methods used to arrive at the solution. This approach will empower you to solve similar problems independently and enhance your problem-solving skills in general.
To effectively solve the tank filling time problem, we first need to dissect the information provided. The core of the problem states that 90 gallons of oil flow through a pipe in 18 minutes. This piece of information is crucial as it gives us the rate of flow, which is the amount of oil that flows per unit of time. In this case, we have the flow rate in gallons per minute, although we'll need to calculate it explicitly. The question then asks how long it will take to fill a 600-gallon tank using this same pipe. This means we need to determine the total time required to accumulate 600 gallons of oil, given the flow rate we derive from the initial information.
Before we jump into calculations, it's essential to recognize the fundamental relationship at play here: the volume of fluid (in gallons) is equal to the flow rate (in gallons per minute) multiplied by the time (in minutes). This relationship is expressed mathematically as:
Volume = Flow Rate × Time
Understanding this equation is the key to solving the problem. We know the volume we want to achieve (600 gallons), and we can calculate the flow rate from the given information (90 gallons in 18 minutes). The remaining step is to solve for the time. By rearranging the equation, we get:
Time = Volume / Flow Rate
This formula will be our guiding light as we proceed with the calculations. It's also important to note any assumptions we're making. We assume that the flow rate remains constant throughout the entire filling process. This means the pipe is delivering oil at a consistent rate, and there are no fluctuations or interruptions in the flow. In real-world scenarios, this might not always be the case, but for the purpose of this problem, we assume a constant flow rate.
The first concrete step in solving our time calculation problem is to determine the flow rate of oil through the pipe. We are given that 90 gallons of oil flow through the pipe in 18 minutes. To find the flow rate, which is the amount of oil flowing per minute, we need to divide the total volume of oil by the time it takes to flow.
Flow Rate = Total Volume / Time
In this case:
Total Volume = 90 gallons Time = 18 minutes
So, the flow rate is calculated as:
Flow Rate = 90 gallons / 18 minutes
Performing this division gives us:
Flow Rate = 5 gallons per minute
This means that the pipe delivers 5 gallons of oil every minute. This is a crucial piece of information because it allows us to relate the volume of oil to the time it takes to fill the tank. Now that we have the flow rate, we can move on to the next step, which involves using this flow rate to calculate the total time required to fill the 600-gallon tank.
Understanding and accurately calculating the flow rate is essential in many practical applications. Whether it's determining the speed at which a pump fills a tank, estimating the flow of water in a river, or calculating the rate at which a chemical reaction proceeds, the concept of flow rate is fundamental. This simple calculation here lays the groundwork for more complex fluid dynamics problems.
Now that we have successfully calculated the flow rate, which is 5 gallons per minute, we are well-equipped to determine the total filling time for the 600-gallon tank. As discussed earlier, the relationship between volume, flow rate, and time is expressed as:
Time = Volume / Flow Rate
We know the volume of the tank we need to fill:
Volume = 600 gallons
And we have calculated the flow rate:
Flow Rate = 5 gallons per minute
Substituting these values into the equation, we get:
Time = 600 gallons / 5 gallons per minute
Performing this division gives us:
Time = 120 minutes
Therefore, it will take 120 minutes to fill the 600-gallon tank using this pipe. This result provides a clear and concise answer to the original question. The calculation is straightforward, but it relies on the accurate determination of the flow rate, which we achieved in the previous step.
This type of calculation is not only applicable to filling tanks with liquids but also to a wide range of scenarios involving rates and quantities. For example, it can be used to estimate the time required to complete a task given a certain work rate, or to calculate the amount of fuel needed for a journey given the fuel consumption rate of a vehicle. The underlying principle remains the same: understanding the relationship between rate, quantity, and time allows us to solve practical problems efficiently.
To solidify our understanding, let's recap the entire step-by-step solution process for this problem:
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Understand the Problem: We are given that 90 gallons of oil flow through a pipe in 18 minutes, and we need to find out how long it will take to fill a 600-gallon tank using the same pipe.
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Calculate the Flow Rate: Divide the total volume of oil (90 gallons) by the time it takes to flow (18 minutes) to find the flow rate.
Flow Rate = 90 gallons / 18 minutes = 5 gallons per minute
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Apply the Formula: Use the formula Time = Volume / Flow Rate to calculate the time required to fill the tank.
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Substitute Values: Substitute the given volume (600 gallons) and the calculated flow rate (5 gallons per minute) into the formula.
Time = 600 gallons / 5 gallons per minute
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Calculate the Time: Perform the division to find the time.
Time = 120 minutes
This step-by-step approach not only provides the answer but also offers a clear roadmap for solving similar problems. By breaking down the problem into smaller, manageable steps, we can avoid confusion and ensure accuracy. Each step builds upon the previous one, leading us to the final solution in a logical and organized manner.
This systematic approach is a valuable skill in problem-solving, regardless of the specific context. Whether you are dealing with mathematical problems, scientific experiments, or everyday challenges, the ability to break down a problem into smaller steps and address each step methodically is a key to success. In the case of this filling time calculation, the steps involved calculating the flow rate and then using that rate to find the total time. This process can be adapted and applied to a wide range of problems involving rates, quantities, and time.
In conclusion, we have successfully determined that it will take 120 minutes to fill a 600-gallon tank if 90 gallons of oil flow through a certain pipe in 18 minutes. This final thoughts and key takeaways summary showcases the problem-solving process involved understanding the given information, calculating the flow rate, and applying the formula Time = Volume / Flow Rate. The step-by-step solution provided a clear and structured approach to the problem, ensuring accuracy and comprehension.
Understanding the relationship between volume, flow rate, and time is a fundamental concept with broad applications. From filling tanks to estimating travel times, this principle underlies many real-world scenarios. The ability to break down a problem into manageable steps and apply the appropriate formulas is a valuable skill that can be applied across various disciplines.
The answer to the question, “If 90 gallons of oil flow through a certain pipe in 18 minutes, how long will it take to fill a 600-gallon tank using this pipe?” is 120 minutes. This solution not only provides the correct answer but also demonstrates a methodical approach to problem-solving, emphasizing the importance of understanding the underlying principles and applying them effectively.
D. 120 minutes
