Two valves, A and B, can fill a water reservoir in 12 and 15 minutes respectively. Both operate simultaneously, but valve A is shut off after 3 minutes. How much additional time is required to completely fill the reservoir?
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Answer: C. 8 1/4 min
Explanation
Valves A and B fill one twelfth and one fifteenth of the reservoir per minute respectively. Working together for three minutes, they fill a combined total of nine twentieths of the total reservoir capacity. The remaining eleven twentieths of the reservoir is filled by valve B alone in eight and one quarter minutes. Individual filling rates are expressed as unit fractions representing the portion of a container filled per minute. Combined filling rates of multiple valves are calculated by summing their individual fractional rates per unit time. Remaining work is determined by subtracting the completed fraction from the whole container capacity of one.
Three and one quarter minutes ignores the work completed during the initial three minute joint operation period. Five and one quarter minutes underestimates the time required for valve B to finish filling the remaining volume. Nine and one quarter minutes overestimates the additional time needed due to an arithmetic error in fraction multiplication.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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