One woman can fill a single bucket completely in 6 minutes. Starting at 8:00 a.m., a total of 1845 buckets must be filled by 9:30 a.m., which is a time span of 1 hour 30 minutes. How many women workers are required so that all 1845 buckets are filled within this time limit?

Introduction / Context:
This question is a direct application of time and work ideas where a fixed number of identical workers must complete a known quantity of identical tasks within a fixed time window. We are told how fast a single woman can fill one bucket and asked to determine how many women are required to fill a large number of buckets within 90 minutes.

Given Data / Assumptions:

• One woman fills 1 bucket in 6 minutes.
• Total number of buckets to be filled = 1845.
• Available time from 8:00 a.m. to 9:30 a.m. = 1 hour 30 minutes = 90 minutes.
• All women work at the same constant rate and can work simultaneously without interfering with each other.

Concept / Approach:
The work unit here is one full bucket. The rate of one woman is buckets per minute. If there are N women, the total rate is N times the rate of one woman. The total work done in the allotted time equals total rate multiplied by time. We equate that to the required 1845 buckets and solve for N, rounding only if necessary. In this problem the number comes out exactly as an integer.

Step-by-Step Solution:
Time taken by one woman to fill 1 bucket = 6 minutes. So, rate of one woman = 1 / 6 buckets per minute. Let N be the required number of women. Total rate for N women = N * (1 / 6) = N / 6 buckets per minute. Available time = 90 minutes. Total buckets filled in 90 minutes = (N / 6) * 90 = 15 N. We need 15 N = 1845 buckets. Therefore, N = 1845 / 15 = 123 women. So 123 women must work together to finish 1845 buckets in the given time.

Verification / Alternative check:
If 123 women work for 90 minutes, each woman fills 90 / 6 = 15 buckets. Multiplying, the total buckets filled equals 123 * 15 = 1845, which is exactly the required number. This confirms that the calculation is correct and that no rounding or approximation is involved.

Why Other Options Are Wrong:
111 women would fill only 111 * 15 = 1665 buckets, which is short of 1845. 117 women would fill 117 * 15 = 1755 buckets, still not enough. 139 women would produce 139 * 15 = 2085 buckets, which is more than required. 129 women would also give 129 * 15 = 1935 buckets, exceeding the target.

Common Pitfalls:
Learners sometimes confuse the time for one bucket with the total time window and try to divide buckets by minutes directly without considering the number of workers. Others may incorrectly convert the time from 1 hour 30 minutes into minutes. Always first convert the full time to minutes, compute the capacity of one worker over that period, then divide the required total work by that capacity to find the number of workers needed.

Final Answer:
A total of 123 women are required to fill 1845 buckets between 8:00 a.m. and 9:30 a.m.