Two inlet pipes A and B can fill a reservoir in 20 and 30 minutes respectively, whereas a third valve C empties it within 40 minutes. What duration is needed to fill the container if all three pipes operate simultaneously?
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Answer: C. 17 1/7 min
Explanation
Inlet pipe rates are one twentieth and one thirtieth while the emptying valve rate is one fortieth per minute. Combining the filling and emptying rates yields six plus four minus three over one hundred twenty. The net rate of seven over one hundred twenty means the container fills in one hundred twenty over seven minutes. Operating inlet and outlet pipes simultaneously requires adding filling rates and subtracting emptying rates. Net work rate represents the actual progress made per unit time when opposing valves are open. The total time to fill a container against an active drain is the reciprocal of the net work rate.
Option a overestimates the fill time due to an arithmetic error in the net rate fraction. Option b calculates a slower fill time by misapplying the outlet valve subtraction. Option d results from an incorrect numerator calculation in the final time fraction inversion.
- Subject
- Mathematics
- Category
- Mathematics
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- —
- Difficulty
- medium
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