Operating two valves concurrently fills the water tank in 12 hours. One valve fills it 10 hours quicker than the alternative valve. How many hours does the faster valve require to fill the tank independently?
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Answer: C. 20 hrs
Explanation
Letting the faster valve take x hours means the slower valve requires x plus ten hours. Setting up their combined work rate equation equals one twelfth based on their joint duration. Solving the resulting algebraic equation reveals twenty hours for the faster valve. Joint rate equations model how multiple mechanical devices share a single workload over time. Inverse time relationships lead to rational equations that simplify into solvable polynomials. Physical time values must be positive real numbers to be considered valid solutions.
Pumping station operations utilize joint rate calculations to schedule equipment maintenance windows. Industrial manufacturing uses machine speed comparisons to optimize factory production schedules. Engineering management applies rate formulas to evaluate equipment efficiency improvements. Option A suggests twenty five hours which fails to satisfy the joint twelve hour equation. Option B proposes twenty eight hours which overestimates the speed of the faster valve. Option D offers thirty five hours which results from an incorrect polynomial solution.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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