Equal amounts of water were poured into two empty jars of different capacities, which made one jar \(\frac{1}{4}\) full and the other jar \(\frac{1}{3}\) full. If the water in the jar with lesser capacity is then poured into the jar with greater capacity, then the part of the larger jar filled with water is:

Calculation of Water Levels in Jars with Different Capacities

This problem presents a scenario where equal volumes of water are introduced into two jars of distinct capacities. Here’s a breakdown of the situation and the outcome when the water from one jar is transferred to the other.

Initial Setup

– Larger Jar: When filled with a certain volume of water, it reaches \(\frac{1}{4}\) of its full capacity.
– Smaller Jar: The same volume of water fills this jar to \(\frac{1}{3}\) of its capacity, indicating its smaller size compared to the larger jar.

Transfer Process and Outcome

Upon transferring the water from the smaller jar (which is \(\frac{1}{3}\) full) into the larger jar (\(\frac{1}{4}\) full), we aim to understand how the water level changes in the larger jar.

– Observation: Since the initial amounts of water in both jars are equal, transferring the water from the smaller jar to the larger one effectively doubles the amount of water in the larger jar.

– Mathematical Representation: The act of pouring water from the smaller jar doubles the water volume in the larger jar, leading to the equation \(2 \times \frac{1}{4} = \frac{1}{2}\).

Conclusion

Therefore, after the water from the smaller jar is poured into it, the larger jar becomes \(\frac{1}{2}\) full.