Two individual pipes can fill a water tank in 60 min and 75 min respectively, while a bottom drain pipe empties it. Activating all three valves concurrently results in the tank filling within 50 min. How much time does the drain pipe alone require to empty the full tank?
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Answer: B. 100 min
Explanation
The individual filling rates of the two inlet pipes are one sixtieth and one seventy fifth per minute. The combined net rate of all three valves running concurrently equals one fiftieth per minute. Subtracting the net rate from the combined inlet rates isolates the drain pipe rate at one one-hundredth. Pipe and cistern problems treat work rates as fractional parts of a tank filled per unit time. Inlet pipes add positive volume rates while bottom drain pipes subtract volume from the container. Solving for an unknown drain rate requires subtracting the net rate from the combined input rates.
Plumbing engineers calculate fill and drain rates to size residential water storage tanks properly. Industrial chemical processing plants use multi valve rate equations to manage tank mixing. Municipal water management relies on flow rate calculations to maintain balanced reservoir levels. Option A suggests ninety minutes which overestimates the emptying speed of the drain. Option C proposes one hundred ten minutes which fails to satisfy the rate equation balance. Option D offers one hundred twenty minutes which underestimates the draining capacity.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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