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13 Jan 2026, 11:56
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Minimum: 17.5
Maximum: 19.5
Alex, Beth, Charles, and Dana, each working alone at their own constant rates, can complete a certain task in 8, 20, 40, and 80 hours, respectively. The project manager will schedule them to work on the task in a repeating four-person cycle in which each person works for exactly one hour before the next person begins.
Select for Minimum the minimum number of hours required for the task to be completed, and select for Maximum the maximum number of hours required for the task to be completed. Make only two selections, one in each column.
Select for Minimum the minimum number of hours required for the task to be completed, and select for Maximum the maximum number of hours required for the task to be completed. Make only two selections, one in each column.
| Minimum | Maximum | |
| 3.5 | ||
| 16 | ||
| 16.5 | ||
| 17.5 | ||
| 18 | ||
| 19.5 |
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Official Answer
Minimum: 17.5
Maximum: 19.5
13 Jan 2026, 11:56
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Official Solution:
Assume the task consists of 80 units of work for simplicity. In this case, in one hour:
• Alex can complete 10 units of work,
• Beth can complete 4 units,
• Charles can complete 2 units,
• Dana can complete 1 unit.
In one cycle, each of them works for one hour, and no matter the order, the total work completed in 4 hours is 10 + 4 + 2 + 1 = 17 units of work.
So, in four full cycles (16 hours), they will complete 4 * 17 = 68 units of work, leaving 12 units remaining.
Minimum time:
To minimize the total time, we need the sequence of workers to be from fastest to slowest. So, it should be Alex, Beth, Charles, and then Dana. In this case, Alex will complete 10 units in one hour, leaving 2 units. Beth, being the next fastest, will complete these 2 units in half an hour.
So, the total minimum time is 16 hours (for the full cycles) + 1 hour (for Alex’s work) + 0.5 hours (for Beth’s work) = 17.5 hours.
Maximum time:
For maximum time, we need the sequence of workers to be from slowest to fastest. So, the order should be Dana, Charles, Beth, and then Alex. Dana, Charles, and Beth together will complete 1 + 2 + 4 = 7 units in 3 hours. The remaining 5 units will be completed by Alex in half an hour.
So, the total maximum time is 16 hours (for the full cycles) + 3 hours (for Dana, Charles, and Beth’s work) + 0.5 hours (for Alex’s work) = 19.5 hours.
Correct answer:
Minimum "17.5"
Maximum "19.5"
Bunuel
Assume the task consists of 80 units of work for simplicity. In this case, in one hour:
• Alex can complete 10 units of work,
• Beth can complete 4 units,
• Charles can complete 2 units,
• Dana can complete 1 unit.
In one cycle, each of them works for one hour, and no matter the order, the total work completed in 4 hours is 10 + 4 + 2 + 1 = 17 units of work.
So, in four full cycles (16 hours), they will complete 4 * 17 = 68 units of work, leaving 12 units remaining.
Minimum time:
To minimize the total time, we need the sequence of workers to be from fastest to slowest. So, it should be Alex, Beth, Charles, and then Dana. In this case, Alex will complete 10 units in one hour, leaving 2 units. Beth, being the next fastest, will complete these 2 units in half an hour.
So, the total minimum time is 16 hours (for the full cycles) + 1 hour (for Alex’s work) + 0.5 hours (for Beth’s work) = 17.5 hours.
Maximum time:
For maximum time, we need the sequence of workers to be from slowest to fastest. So, the order should be Dana, Charles, Beth, and then Alex. Dana, Charles, and Beth together will complete 1 + 2 + 4 = 7 units in 3 hours. The remaining 5 units will be completed by Alex in half an hour.
So, the total maximum time is 16 hours (for the full cycles) + 3 hours (for Dana, Charles, and Beth’s work) + 0.5 hours (for Alex’s work) = 19.5 hours.
Correct answer:
Minimum "17.5"
Maximum "19.5"
01 Mar 2026, 07:30
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Hey i really didnt understand the II Part of the question
For maximum time, we need the sequence of workers to be from slowest to fastest. So, the order should be Dana, Charles, Beth, and then Alex. Dana, Charles, and Beth together will complete 1 + 2 + 4 = 7 units in 3 hours. The remaining 5 units will be completed by Alex in half an hour.
So, the total maximum time is 16 hours (for the full cycles) + 3 hours (for Dana, Charles, and Beth’s work) + 0.5 hours (for Alex’s work) = 19.5 hours.
Could you please elaborate how are you calculating time
For maximum time, we need the sequence of workers to be from slowest to fastest. So, the order should be Dana, Charles, Beth, and then Alex. Dana, Charles, and Beth together will complete 1 + 2 + 4 = 7 units in 3 hours. The remaining 5 units will be completed by Alex in half an hour.
So, the total maximum time is 16 hours (for the full cycles) + 3 hours (for Dana, Charles, and Beth’s work) + 0.5 hours (for Alex’s work) = 19.5 hours.
Could you please elaborate how are you calculating time
