One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill the tank in 36 minutes, then the slower pipe alone will be able to fill the tank in

### Concept & Relative Efficiency If a pipe is $n$ times faster than another, its efficiency is $n$ times that of the slower pipe. Time and efficiency are inversely proportional. Total work can be assumed as Total Efficiency $\times$ Total Time. $$ \text{Total Work} = (\text{Efficiency}_1 + \text{Efficiency}_2) \times \text{Time Together} $$ ### Step-by-Step Solution 1. **Define Efficiencies:** * Let the efficiency of the slower pipe = 1 unit/min. * The faster pipe is 3 times as fast, so its efficiency = 3 units/min. 2. **Calculate Total Efficiency:** * Combined efficiency of both pipes = $1 + 3 = 4$ units/min. 3. **Determine Total Work (Tank Capacity):** * They fill the tank together in 36 minutes. * Total Capacity = Combined Efficiency $\times$ Time = $4 \times 36 = 144$ units. 4. **Calculate Time for Slower Pipe:** * Time taken by slower pipe = $\frac{\text{Total Capacity}}{\text{Efficiency of Slower Pipe}}$ * Time = $\frac{144}{1} = 144$ minutes. ### Exam Strategy & Shortcut Think purely in ratios. Speed ratio = 3:1. Total speed = 4. The slower pipe's speed is 1 out of the total 4. Therefore, it will take 4 times as long as the combined time. $36 \text{ mins} \times 4 = 144 \text{ mins}$. ### Common Pitfall Students often set up a time equation as $x + 3x = 36$, completely misinterpreting the relationship between time and speed. The correct time relationship is $\frac{1}{x} + \frac{1}{3x} = \frac{1}{36}$. The efficiency method avoids fractions entirely. ### Final Answer Therefore, the correct answer is **144 min**.