Filling a Tank: A Simple Math Problem and Real-World Application

Suppose you have a water tank, and a pump continuously fills it with 1200 liters of water. However, after the pump finishes, the tank still has 60 liters empty. How much more water is required to completely fill the tank?

Understanding the Problem

This scenario presents a classic problem in basic algebra, requiring an understanding of proportions and simple arithmetic. Let's break it down step by step.

Calculate the Total Capacity of the Tank

We know that 1200 liters is 40% of the total capacity of the tank. This means the tank is currently 40% full. Let's denote the total capacity of the tank as C.

The equation to find the total capacity is:

0.4C 1200 (litres)

Solving for C:

C 1200 / 0.4 3000 litres

Calculate the Current Water Volume

Since the tank can hold 3000 liters and is currently 40% full, the volume of water in the tank is:

Water currently in the tank 0.4 × 3000 1200 litres

Determine the Additional Water Needed

The tank needs to be 100% full to be completely filled. The current volume is 1200 liters, so the amount of water needed is:

Water needed 3000 - 1200 1800 litres

Extending the Problem: Real-World Considerations

In the world of practical applications, the problem of calculating water volume is relatively straightforward. However, in real-world scenarios, additional considerations are indeed necessary:

Measurement of 1200 Liters

How do we determine that 1200 liters were initially pumped into the tank? In a real-world setting, this would require an accurate measuring device, such as a flow meter or tank gauge, to ensure that the correct amount of water was dispensed.

Measurement of Remaining Water

Similarly, to fill the tank to the brim, we need to measure the remaining volume, which can also be achieved using tools like a measuring tape, ultrasonic level meters, or direct observation from a filled reference line.

Solution Verification

The original poster suggests a simple ratio approach, which is mathematically sound. To verify the solution, you can:

Utilize a measuring tool to ensure the pump’s output matches the calculated 1200 liters. Use the same tools to confirm the remaining volume. Culminate the process with a physical check to ensure the tank is indeed full.

Conclusion

In conclusion, we have determined that to completely fill the tank, an additional 1800 liters of water is required. This simple problem highlights the importance of mathematical reasoning and practical measurement in ensuring accurate volume management, which is crucial in various fields such as agriculture, construction, and water supply systems.