Three identical pipes can fill 3 buckets of water in 3 hours when all are opened together. Approximately how many buckets of water can 2 of these pipes fill if they are opened together for 2 hours?

Introduction / Context:
This problem tests proportional reasoning in work and time situations. Instead of dealing with tank capacities and complex fractions, it works with bucketfuls of water and identical pipes. The situation is essentially a direct proportion between the number of pipes, time in hours and total work done in terms of buckets filled. Such questions appear frequently in aptitude tests to check if students can scale work rates correctly.

Given Data / Assumptions:

Three identical pipes, when opened together, fill 3 buckets of water in 3 hours.

We are asked about the number of buckets filled by 2 of these pipes running together for 2 hours.

Each pipe is assumed to have a constant and equal rate of flow.

The capacity of each bucket is identical and fixed.

Concept / Approach:
The key concept is that work done = rate * time. For identical pipes, the combined rate is simply the number of pipes multiplied by the rate of one pipe. First, we determine the rate of a single pipe in buckets per hour. Then we scale this rate for 2 pipes and for a different duration. No complicated algebra is required; it is a simple proportion once the single pipe rate is known.

Step-by-Step Solution:
Let the rate of each pipe be r buckets per hour.Three pipes together work at a rate of 3r buckets per hour.Given that 3 pipes fill 3 buckets in 3 hours, the total work is 3 buckets.So 3r * 3 = 3.This simplifies to 9r = 3, so r = 3/9 = 1/3 bucket per hour per pipe.Now consider 2 pipes working together.Combined rate of 2 pipes = 2 * (1/3) = 2/3 bucket per hour.Time given = 2 hours.Work done = rate * time = (2/3) * 2 = 4/3 buckets.
Verification / Alternative check:
We can also think proportionally. Three pipes for 3 hours means a total of 9 pipe hours producing 3 buckets.So 1 pipe hour produces 3/9 = 1/3 bucket.Two pipes for 2 hours means 4 pipe hours.At 1/3 bucket per pipe hour, 4 pipe hours give 4/3 buckets, confirming the result.
Why Other Options Are Wrong:
2/3 bucket and 1 bucket both underestimate the work done by two pipes over two hours; they correspond to misusing time or pipe count in the proportion. Two buckets and 3/2 buckets are overestimates compared with the correct proportional scaling. Only 4/3 buckets is consistent with the basic rate calculation from the original 3 pipes in 3 hours scenario.

Common Pitfalls:
Learners sometimes mistakenly divide 3 buckets by 3 pipes or by 3 hours incorrectly, or they handle only one of the changes (number of pipes or time) instead of both. Another typical error is to assume that if 3 pipes give 3 buckets in 3 hours, then 2 pipes should give 2 buckets in 3 hours, which ignores the linear scaling. Carefully tracking the relation work = rate * time, and identifying how rate changes when the number of pipes changes, prevents such mistakes.

Final Answer:
Approximately 4/3 buckets of water can be filled by 2 pipes running for 2 hours.