Two valves A and B fill a reservoir in 37 1/2 minutes and 45 minutes respectively. Opening both valves, the reservoir achieves full capacity in exactly half an hour provided valve B is closed after how long?
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Answer: B. 9 min
Explanation
Valve A runs for the entire duration of thirty minutes, filling four fifths of the total tank capacity. The remaining one fifth of the tank capacity must be filled by valve B before it is closed. Valve B fills this remaining one fifth portion in exactly nine minutes based on its forty five minute rate. Individual valve filling rates are determined by taking the reciprocal of the total time required to fill the tank. Fractional contributions are calculated by multiplying the running time of each valve by its respective filling rate. Remaining tank capacity is found by subtracting the volume filled by continuously running valves from the whole.
Five minutes underestimates the time valve B needs to fill the remaining fraction of the reservoir capacity. Ten minutes overestimates the required operating time for valve B by a small arithmetic calculation margin. Fifteen minutes assumes valve B ran for half the total duration rather than the precise fraction calculated.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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