P takes twice as long as Q or thrice as long as R to complete a task. Working together, they finish it in 2 days. How long will Q take working independently?
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Answer: D. 6
Explanation
The combined working rate of all three participants equals one half per day. Relating individual speeds reveals that Q completes the task in exactly six days. Working together accelerates the completion time significantly compared to working alone. Let Q take x days, meaning P takes 2x days and R takes 2x/3 days. The individual daily rates are 1/(2x) for P, 1/x for Q, and 3/(2x) for R. Adding the three rates together gives the combined rate of 1/2 work per day.
Collaborative task scheduling is essential in project management and construction logistics. Knowing individual productivity helps managers assign correct staffing levels for deadlines. This mathematical formulation applies directly to multi-worker engineering scenarios. Choosing 7 days fails to satisfy the combined rate equation for the three workers. Choosing 8 days creates a fractional discrepancy when verifying individual proportions. Choosing 9 days results in a combined completion time that is much too slow.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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