An aircraft fuel storage tank can be filled by Pump A in 6 hours and by Pump B in 8 hours. Due to a drain leak valve at the bottom, Pump A and Pump B operating together take 4 hours to completely fill the empty tank. How many hours would the leak alone take to completely empty a full tank?

Answer Key:

24

### 5-Stage Derivation & Analytical Solution: 1. **Stage 1: Individual Filling Rates:** * Rate of Pump A: $R_A = 1/6\text{ tank/hr}$. * Rate of Pump B: $R_B = 1/8\text{ tank/hr}$. 2. **Stage 2: Net Combined Rate with Leak Rate $R_L$:** * $R_A + R_B - R_L = \frac{1}{T_{net}} = \frac{1}{4\text{ hr}}$. 3. **Stage 3: Solving for $R_L$:** * $\frac{1}{6} + \frac{1}{8} - R_L = \frac{1}{4}$. * Common denominator is 24: * $\frac{4}{24} + \frac{3}{24} - R_L = \frac{6}{24}$. * $\frac{7}{24} - R_L = \frac{6}{24} \implies R_L = \frac{7 - 6}{24} = \frac{1}{24}\text{ tank/hr}$. 4. **Stage 4: Time to Empty Full Tank:** Time $= 1 / R_L = 24\text{ hours}$. 5. **Stage 5: Official Reference:** Standard Engineering Quantitative Aptitude (Work & Rate mechanics).

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