1. **State the problem:** We need to find the input horsepower (HP) required to drive a compressor delivering 5,389 SCFM at 40.6 psia with an overall efficiency of 84%. 2. **Relevant formula:** The power required for a compressor can be estimated using the formula: $$\text{Power input} = \frac{\text{Power output}}{\text{Efficiency}}$$ 3. **Calculate power output:** Power output depends on the flow rate, pressure, and gas properties. Since specific gas properties are not given, we assume the power output is proportional to the product of pressure and volumetric flow rate. 4. **Convert flow rate and pressure to consistent units:** SCFM is standard cubic feet per minute, and psia is absolute pressure. We use the formula for power in horsepower: $$HP = \frac{144 \times P \times V}{(\text{Efficiency} \times 33000)}$$ where $P$ is pressure in psi, $V$ is volumetric flow rate in cubic feet per minute, 144 converts psi to lb/ft², and 33000 ft-lb/min is 1 HP. 5. **Calculate power output:** $$HP_{output} = \frac{144 \times 40.6 \times 5389}{33000} = \frac{314,927.616}{33000} = 9.54$$ 6. **Calculate input power considering efficiency:** $$HP_{input} = \frac{HP_{output}}{0.84} = \frac{9.54}{0.84} = 11.36$$ 7. **Final answer:** The input horsepower required is **11.36 HP**.