A rotary drum filter that is $6 \mathrm{ft}$ in diameter and $8 \mathrm{ft}$ long is to be used to filter a slurry. The drum rotates at $0.5 \mathrm{rpm}$, and one-third of the drum's surface is submerged under the slurry. A vacuum is drawn in the drum so that a constant pressure drop of $10 \mathrm{psi}$ is maintained across the drum and filter cake. You test the slurry in the lab by pumping it at a constant filtrate rate of $20 \mathrm{gpm}$ through $1 \mathrm{ft}^{2}$ of the drum filter screen and find that after $1 \mathrm{~min}$ the pressure drop is 8 psi and after $3 \mathrm{~min}$ the pressure drop is $12 \mathrm{psi}$. How long will it take to filter 100,000 gal of the filtrate from the slurry using the rotary drum?