A natural gas (methane) pipeline is designed to transport the gas at a rate of $5000 \mathrm{scfm}$. The pipe is $6 \mathrm{in}$. ID and the maximum pressure that the compressors can develop is $1500 \mathrm{psig}$. The compressor stations are located in the pipeline at the point at which the pressure drops to $100 \mathrm{psi}$ above that at which choked flow would occur (i.e., the suction pressure for the compressor stations). If the design temperature for the pipeline is $60^{\circ} \mathrm{F}$, the compressors are $60 %$ efficient, and the compressor stations each operate with three stages and interstage cooling to $60^{\circ} \mathrm{F}$, determine

(a) The proper distance between compressor stations, in miles

(b) The optimum interstage pressure and compression ratio for each compressor stage

(c) The total horsepower required for each compressor station