Question 965451
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The inlet fills 1 pool /6 hours=(1/6) pool/hr
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The drain empties -1 pool /12 hours=-(1/12) pool/hour
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Net change with both open=+(1/6) pool/hr-(1/12) pool/hr=+(1/12) pool/hr
With both open. the pool fills at a rate of 1/12 pool/hr.
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If the pool is 1/4 (3/12) full, that leaves ((1)-(3/12)=9/12) 9/12 pool to fill, at a rate of 1/12 pool/hr it will take 9 hours.
ANSWER: With both pipes open, it takes 9 hours to fill 3/4 of the pool.