Two valves P and Q fill a container in 12 and 15 minutes respectively. Opening both together, the first valve is deactivated after 3 minutes. How much additional time is needed to completely fill the container?
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Answer: B. 11 1/4 min
Explanation
Valves P and Q fill one twelfth and one fifteenth of the container per minute respectively. Operating together for three minutes, they fill a combined total of nine twentieths of the container capacity. The remaining eleven twentieths of the container is filled by valve Q alone in eight and one quarter minutes, totaling eleven point two five minutes. Individual valve filling rates are represented as fractional parts of the container filled per minute of operation. Combined rates for multiple active valves are determined by adding their individual unit fractions together. Total completion time includes both the initial joint operating duration and the subsequent single valve running time.
Nine and one quarter minutes fails to include the initial three minute joint operating period in the total time sum. Seven and one quarter minutes underestimates the total duration required to complete the container filling process. Eight and one half minutes accounts only for the secondary filling phase while omitting the initial operating period.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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