When dealing with problems related to capacity and volume, it is important to understand the relationships between the given information and the desired answer. This article explains how to determine the capacity of a water tank given that 2/3 of its volume is 2400 liters, and how different scenarios can alter the final answer. Let's explore the mathematical reasoning behind this problem and the key principles involved.

Introduction

A common problem in water management and engineering involves determining the total capacity of a water tank based on the volume of water currently contained within it. This article will walk through the steps to solve such a problem and highlight the importance of accurate calculations in real-world applications. We'll use the example of a water tank that is 2/3 full with a volume of 2400 liters to find the total capacity of the tank.

Understanding the Problem

The problem statement states that a water tank is 2/3 full, and its current volume is 2400 liters. We need to find the total capacity of the tank, denoted as (x).

Mathematical Approach

To solve this problem, we can set up a proportion based on the given information:

Represent the total capacity of the tank as (x) liters. Since 2/3 of (x) is 2400 liters, we can write the equation: ( frac{2}{3} x 2400 ) To find the value of (x), we can rearrange the equation to solve for (x): ( x 2400 times frac{3}{2} ) ( x 3600 ) liters

Therefore, the capacity of the water tank is 3600 liters. This solution is widely accepted and aligns with the claim made by Peter, supporting his assertion.

Alternative Scenarios

It is crucial to consider different scenarios that could affect the final answer. For instance, if there is a doubt about the current measurement (2400 liters) rather than Peter's claim, further investigation might be necessary to verify the accuracy of the given volume. Independent measurements can provide additional confidence in the solution.

On the contrary, if we blindly trust the current measurement but doubt Peter's claim, we would need to analyze the situation more critically. In the given example, if the current volume of 2400 liters is considered correct, and assuming the tank can hold more, Peter's claim of 3600 liters seems plausible. However, if the tank is visibly unable to contain more than 2400 liters, then the initial measurement might be more reliable.

Conclusion

To determine the capacity of a water tank, accurately interpreting the given information is essential. In the example provided, the capacity of the tank is 3600 liters, validating Peter's claim. However, in real-world scenarios, it is crucial to validate measurements through multiple means to ensure the accuracy of the calculations and the reliability of the claims.

For further exploration, you can explore similar problems in basic mathematics, such as determining the volume of other containers or solving more complex engineering problems involving fluid dynamics and tank sizing.