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good morning, I studying to take my exam, have a math question that is fooling me some. Question as follows,

A belt filter press receives a feed sludge at 3% total solids and produces a cake that is 20% total solids. If influent flow rate to the press is 50 GPM, what will the volume of cake produce be if the press runs for 10 hours?

I thank you very much for your time and help, again thank you.

The way I figure it is that the filter press is able to squeeze out enough water to produce a 20% solid component flow (cake) from a 3% flow (sludge). This assumes that the press captures all the waste solids.

Converting percents to fractions, i.e., 3% -> 0.03 and 20% -> 0.20, this means that the cake has a volume (0.03/0.20) = 0.15 as much as the sludge. That is, the same amount of solids make up the 2 fractions of solids, which means the volume for the 20% must be less than for the 3%.

Using this fraction, we have the production of cake = (0.15)(50 GPM) = 7.5 GPM.

Now, 10 hours converts to (10 hours)(60 min/hour) = 600 minutes.

Thus the total amount of cake produced in 10 hours is (600 min)(7.5 GPM) = 4500 gal.
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#### randy patton

##### Expertise

college mathematics, applied math, advanced calculus, complex analysis, linear and abstract algebra, probability theory, signal processing, undergraduate physics, physical oceanography

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26 years as a professional scientist conducting academic quality research on mostly classified projects involving math/physics modeling and simulation, data analysis and signal processing, instrument development; often ocean related

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J. Physical Oceanography, 1984 "A Numerical Model for Low-Frequency Equatorial Dynamics", with M. Cane

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M.S. MIT Physical Oceanography, B.S. UC Berkeley Applied Math

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