Question 375970: Pipe A fills the pool in 4 hrs. while pipe B drains it in 7 hours. If both pipes were open, how long will it take to fill the pool?
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! This type of work problem requires you to think about doing the whole job as 100% done in some amount of time, 't'.
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Pipe A fills the pool in 4 hr, so it is operating at a rate of 1/4 of a full pool per hr, or 25% per hr.
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Pipe B drains it in 7 hr, so it is operating at a rate of -1/7 of a full pool per hr, or about -14.3% per hr.
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With both running full tilt, the net rate of filling the pool is 25% per hr - 14.3% per hr = 10.7% per hr.
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Given 't' = time, we now need to know how long it takes to total 100%.
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.107t = 1
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Multiply both sides by 1000 to remove the decimal.
107t = 1000
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Divide both sides by 107.
t = 1000/107 = 9.346
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That means it will take 9.346 hrs to fill the pool with both pipes flowing at full capacity.
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Always check your work!
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9.346 hr * 25% = 2.3365
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9.346 hr * -14.3% = -1.3365
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Adding these two, we have 1.0 left over, which means the pool is full!
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Done.
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