If a learner completes q problems within 1/h hours, how many total problems can she finish at this pace during q hours?
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Answer: B. hq2
Explanation
Dividing the number of problems q by the fractional hour value determines the hourly work rate. The hourly rate simplifies to h times q problems completed per unit of time. Multiplying the hourly rate by the total duration q hours yields h times q squared total problems. Work rate is calculated by dividing total output quantity by the time duration required. Algebraic expressions can be manipulated by multiplying rates by varying time periods. Fractions in denominators invert when dividing quantities in algebraic fraction simplification.
Productivity analysis in manufacturing uses rate formulas to measure output efficiency over time. Academic pacing calculations help students estimate study workloads across extended time blocks. Project management applications track task completion rates to forecast overall project completion. Option A suggests h q which misses multiplying by the second time variable. Option C proposes one over h q which inverts the rate calculation incorrectly. Option D offers h over q which represents an invalid algebraic manipulation of the variables.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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