Two valves fill a tank in 20 and 24 minutes respectively, while a drainage valve drains 3 gallons per minute. Activating all three valves simultaneously fills the basin in 15 minutes. What is the basin's total water volume capacity?
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Answer: C. 120 gallons
Explanation
The combined operating rate of all three valves running simultaneously fills the basin in fifteen minutes. Calculating the individual filling rates and factoring the drain yields the net volume contribution per minute. Multiplying the net operational flow by fifteen minutes establishes the total water volume capacity of one hundred twenty gallons. Valve one fills the tank in twenty minutes while valve two completes the task in twenty-four minutes. The drainage valve removes three gallons of water per minute throughout the entire operational duration. Algebraic summation of all active flow rates allows determination of the unknown total tank capacity.
Option A suggests sixty gallons which underestimates the total volume capacity derived from the flow rates. Option B proposes one hundred gallons which fails to satisfy the simultaneous valve operating equations. Option D implies one hundred eighty gallons which overstates the volume calculated from the fifteen-minute duration.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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