A rotary drum filter, $10 \mathrm{ft}$ in diameter and $8 \mathrm{ft}$ long, is to be used to filter a slurry of incompressible solids. The drum rotates at $1.2 \mathrm{rpm}$, and $40 %$ of its surface is submerged beneath the slurry at all times. A vacuum in the drum maintains a constant pressure drop of $10 \mathrm{psi}$ across the drum and filter cake. The slurry is tested in the lab by pumping it at a constant rate of $5 \mathrm{gpm}$ through $0.5 \mathrm{ft}^{2}$ of the drum filter screen. After $1 \mathrm{~min}$, the pressure drop is $9 \mathrm{psi}$, and after $3 \mathrm{~min}$ it has risen to 15 psi. How long will it take to filter 1 million gal of the filtrate from the slurry using the rotary drum? How long would it take if the drum rotated at $3 \mathrm{rpm}$ ?