Tank Filling Problem Calculating Gallons Needed For 135 Liters, 13.5 Liter Gallons

This math problem presents a practical scenario: determining how many gallons of a specific size are needed to fill a tank of a given capacity. To solve this, we'll need to understand the relationship between liters and gallons, perform some unit conversions, and then apply basic division. Let's break down the problem step by step.

Understanding the Problem: Tank Capacity and Gallon Size

At the heart of this problem lies a simple question with practical implications: How many gallons does it take to fill a tank? We are given the tank's capacity, which is 135 liters. We also know that the girl is using gallons that each hold $13 rac{1}{2}$ liters. Our goal is to find out how many of these gallons are needed to completely fill the tank.

This is a classic example of a division problem where we are trying to find out how many times a smaller quantity (the gallon's capacity) fits into a larger quantity (the tank's capacity). To solve this, we will divide the total volume of the tank by the volume of each gallon. Before we can do that, we need to make sure we are working with consistent units. In this case, both volumes are already expressed in liters, so we can proceed with the calculation.

This problem highlights the importance of understanding units and how they relate to each other. In everyday life, we often encounter situations where we need to convert between different units of measurement, such as liters and gallons, or meters and feet. Being able to perform these conversions accurately is essential for solving practical problems.

Step-by-Step Solution: Calculating the Number of Gallons

To find out how many gallons are needed to fill the 135-liter tank, we need to perform a simple division. We will divide the total capacity of the tank (135 liters) by the capacity of one gallon ( $13 rac{1}{2}$ liters). This will give us the number of gallons required. Let's do the math:

1. Convert the mixed fraction to an improper fraction:

   13 rac{1}{2} = rac{(13 imes 2) + 1}{2} = rac{26 + 1}{2} = rac{27}{2}

   So, each gallon has a capacity of $rac{27}{2}$ liters.

2. Divide the tank's capacity by the gallon's capacity: Number of gallons = $rac{135}{rac{27}{2}}$

   To divide by a fraction, we multiply by its reciprocal:

   Number of gallons = $135 imes rac{2}{27}$

3. Simplify the expression: Number of gallons = $rac{135 imes 2}{27} = rac{270}{27}$

4. Perform the division: Number of gallons = 10

Therefore, it will take 10 gallons of water to fill the 135-liter tank.

This step-by-step solution illustrates the importance of breaking down a problem into smaller, manageable steps. By converting the mixed fraction to an improper fraction, and then applying the rule for dividing by a fraction, we were able to arrive at the correct answer. This approach can be applied to a wide range of mathematical problems.

Real-World Applications: Why This Matters

This type of calculation has numerous real-world applications. Imagine you are filling a swimming pool, watering a garden, or even cooking a large meal. In all these scenarios, you might need to calculate how much liquid is required to fill a container or meet a specific need. Understanding how to perform these calculations accurately can save you time, money, and prevent potential errors.

For example, if you are filling a swimming pool, you need to know the pool's capacity and the flow rate of your water source. This will allow you to estimate how long it will take to fill the pool and how much water you will need. Similarly, if you are watering a garden, you need to know the water requirements of your plants and the output of your watering system. This will help you to water your plants efficiently and avoid overwatering or underwatering.

In the context of cooking, understanding liquid measurements is crucial for following recipes accurately. Many recipes call for specific amounts of liquids, such as water, milk, or broth. Being able to convert between different units of measurement, such as cups, liters, and gallons, is essential for successful cooking.

This simple math problem, therefore, has far-reaching implications in our daily lives. By mastering the basic concepts of unit conversion and division, we can become more efficient and effective in a variety of tasks.

Conclusion: The Power of Mathematical Problem-Solving

In conclusion, to fill a 135-liter tank using gallons with a capacity of $13 rac{1}{2}$ liters, you would need 10 gallons of water. This problem demonstrates the practical application of basic mathematical concepts such as fractions, division, and unit conversion. By breaking down the problem into smaller steps and applying the appropriate formulas, we were able to arrive at the correct solution.

This exercise highlights the importance of mathematical problem-solving skills in everyday life. Whether it's calculating the amount of liquid needed to fill a tank, estimating the cost of a project, or managing your finances, math plays a crucial role in our ability to make informed decisions and solve practical problems. By developing a strong foundation in mathematics, we can empower ourselves to navigate the world around us more effectively.

The ability to approach a problem systematically, break it down into smaller parts, and apply the appropriate mathematical tools is a valuable skill that can be applied to a wide range of situations. This problem-solving process is not only useful in mathematics but also in other fields such as science, engineering, and even the arts. By mastering these skills, we can become more creative, innovative, and successful in our endeavors.

Original Keyword: A tank has a capacity of 135 liters. A girl wants to fill the tank with water using a gallon of capacity $13 rac{1}{2}$ liters. How many gallons of water will fill the tank?

Repaired and Clearer Keyword: How many gallons of water, each with a capacity of 13.5 liters, are needed to fill a 135-liter tank?

Tank Filling Problem Calculating Gallons Needed for 135 Liters 13.5 Liter Gallons