Calculating Time To Pump 1377000 Litres Of Water

Introduction

In this article, we'll delve into a practical problem involving water pumps and time calculations. We aim to determine how long it takes an engine to pump a substantial amount of water, specifically 1,377,000 liters, given its pumping rate. This is a common type of problem that combines basic arithmetic with unit conversions, making it relevant to various real-world scenarios. Understanding how to approach such problems enhances our ability to estimate and plan tasks involving fluid transfer, whether in industrial, agricultural, or even domestic contexts. We will break down the problem step-by-step, ensuring clarity and accuracy in our calculations. By the end of this discussion, you'll have a solid understanding of the methods used to solve this type of problem and be able to apply them confidently in similar situations. So, let's embark on this mathematical journey and unravel the solution together.

Problem Statement

Our central problem revolves around an engine that pumps water at a constant rate. The engine's capacity is such that it can pump 850 liters of water in a single minute. The challenge is to calculate the total time required for this engine to pump out 1,377,000 liters of water. This problem requires us to utilize basic arithmetic operations, specifically division, and unit conversions to transform minutes into hours. Understanding this kind of problem is useful in numerous practical scenarios, such as planning water supply for irrigation, estimating the time required to empty a pool, or managing water drainage in industrial settings. Solving it involves not just the mathematical operation but also the conceptual understanding of rates and proportions. This article will guide you through a detailed solution, making sure you grasp each step and its significance. Let's begin by outlining the known information and then formulating a plan to solve this intriguing question.

Step-by-Step Solution

To solve this problem effectively, we need to break it down into manageable steps. This methodical approach not only makes the problem easier to understand but also reduces the chances of errors in our calculations. First, we need to determine the total time in minutes required to pump 1,377,000 liters of water. Given that the engine pumps 850 liters per minute, we can find the total time in minutes by dividing the total volume of water by the pumping rate. This step involves a simple division operation, but it's crucial as it sets the foundation for the rest of the solution.

Next, once we have the total time in minutes, we need to convert it into hours. Since there are 60 minutes in an hour, we can perform this conversion by dividing the total time in minutes by 60. This conversion is a fundamental step, as the problem requires the answer in hours, and minutes are not the desired unit. It’s also important to ensure that we round off the answer appropriately, depending on the level of precision required. By following these steps diligently, we can arrive at the correct solution and express the answer in the desired unit. Let's dive into the calculations to solidify our understanding.

Calculating Total Time in Minutes

To calculate the total time in minutes, we will divide the total volume of water to be pumped (1,377,000 liters) by the rate at which the engine pumps water (850 liters per minute). This calculation will give us the total number of minutes required to pump the entire volume of water. The formula for this calculation is:

\text{Total Time in Minutes} = \frac{\text{Total Volume of Water}}{\text{Pumping Rate}}

Substituting the given values, we get:

\text{Total Time in Minutes} = \frac{1,377,000 \text{ liters}}{850 \text{ liters/minute}}

Performing this division will yield the total time in minutes. It's a straightforward calculation, but accuracy is key. A slight error in this step can affect the final answer. So, we need to ensure that we perform the division correctly, paying attention to the decimal places if any. Once we have the total time in minutes, we can proceed to the next step, which involves converting this time into hours. This conversion is essential to provide the answer in the units requested in the problem statement. So, let's move forward and convert the minutes into hours.

Converting Minutes to Hours

After calculating the total time in minutes, the next step is to convert this time into hours. Since there are 60 minutes in an hour, we can convert minutes to hours by dividing the total number of minutes by 60. This conversion is a fundamental concept in time calculations and is essential for providing the answer in the correct units. The formula for this conversion is:

${ \text{Total Time in Hours} = \frac{\text{Total Time in Minutes}}{60} }$

This simple division allows us to express the time in a more understandable and commonly used unit. Understanding how to convert between different units of time is a valuable skill in various real-life situations, from scheduling tasks to planning travel times. In this particular problem, the conversion is crucial because the question asks for the answer in hours. Once we perform this division, we will have the final answer in hours, which we can then present as the solution to the problem. Let's proceed with the calculation and determine the total time in hours required to pump 1,377,000 liters of water.

Calculation

Now, let's perform the actual calculations to arrive at the final answer.

First, we calculate the total time in minutes:

${ \text{Total Time in Minutes} = \frac{1,377,000 \text{ liters}}{850 \text{ liters/minute}} = 1620 \text{ minutes} }$

This calculation shows that it takes 1620 minutes for the engine to pump 1,377,000 liters of water. This is a significant amount of time, but to better understand it, we need to convert it into hours.

Next, we convert the total time from minutes to hours:

${ \text{Total Time in Hours} = \frac{1620 \text{ minutes}}{60} = 27 \text{ hours} }$

Therefore, it will take the engine 27 hours to pump 1,377,000 liters of water. This calculation clearly demonstrates how we can use basic arithmetic and unit conversions to solve practical problems. The step-by-step approach ensures that we arrive at the correct answer and understand the process thoroughly. Let's now summarize our findings and present the final answer.

Final Answer

After performing the calculations, we have arrived at the final answer. It will take the engine 27 hours to pump 1,377,000 liters of water. This result is obtained by first calculating the total time in minutes and then converting it to hours. The calculation involved dividing the total volume of water (1,377,000 liters) by the pumping rate (850 liters per minute) to get the time in minutes (1620 minutes). Then, we divided the total minutes by 60 to convert it into hours, resulting in 27 hours.

This problem highlights the importance of understanding rates and unit conversions in practical scenarios. It also demonstrates how breaking down a problem into smaller, manageable steps can make it easier to solve. The answer, 27 hours, provides a clear understanding of the time frame required for the engine to complete the task. This information can be crucial for planning and resource management in various applications. With a clear final answer in hand, let's reflect on the key steps and takeaways from this problem-solving exercise.

Conclusion

In conclusion, we have successfully calculated the time required for an engine to pump 1,377,000 liters of water, given its pumping rate of 850 liters per minute. The problem was solved by first determining the total time in minutes and then converting it to hours. This process involved basic arithmetic operations and a clear understanding of unit conversions. The final answer, 27 hours, provides a practical understanding of the time scale involved in such a task.

This exercise underscores the importance of mathematical skills in everyday problem-solving. The ability to calculate rates, perform unit conversions, and break down complex problems into simpler steps is invaluable in various fields, from engineering to logistics. Furthermore, this problem illustrates the significance of accuracy in calculations and the need to double-check each step to avoid errors. By following a structured approach, we can confidently tackle similar problems and apply these skills in real-world scenarios. Understanding such calculations not only enhances our mathematical proficiency but also equips us with practical knowledge applicable to numerous situations.