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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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