P works twice as fast as Q. Given Q alone finishes a task in 12 days, how many days will P and Q require combined________days
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Answer: D. 4
Explanation
Worker Q finishes the task alone in twelve days, which means P takes half that time at six days. The individual work rates are one twelfth for Q and one sixth for P. Adding their rates gives three twelfths, simplifying to one fourth, which means four days combined. Efficiency ratios state that working twice as fast cuts the required completion time in half. Combined work rates equal the sum of individual reciprocal completion times for all active workers. Inverting the combined work rate fraction yields the total number of days required for completion.
Resource allocation models assign faster workers to tasks to minimize overall project completion schedules. Hiring decisions in contracting rely on productivity multipliers to estimate team completion speeds. Manufacturing efficiency metrics compare worker output speeds to optimize labor force deployments. Option A severely underestimates the required time by miscalculating the sum of unit fractions. Option B represents a premature calculation step rather than the final combined completion time. Option C results from an error when adding the individual fractional work rates together.
- Subject
- Mathematics
- Category
- Mathematics
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- —
- Difficulty
- medium
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