Subjects algebra

Pipe Efficiency

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1. **State the problem:** We have three pipes A, B, and C that fill a tank in different times: Pipe A in 2 hours, Pipe B in 1 hour 30 minutes, and Pipe C in 2 hours 30 minutes. We want to find which pipe(s) is/are more efficient. 2. **Convert all times to hours:** - Pipe A: 2 hours - Pipe B: 1 hour 30 minutes = 1.5 hours - Pipe C: 2 hours 30 minutes = 2.5 hours 3. **Calculate the filling rate of each pipe:** The efficiency is the rate of filling, which is the reciprocal of the time taken. - Pipe A rate: $\frac{1}{2} = 0.5$ tanks per hour - Pipe B rate: $\frac{1}{1.5} = \frac{2}{3} \approx 0.6667$ tanks per hour - Pipe C rate: $\frac{1}{2.5} = 0.4$ tanks per hour 4. **Compare the rates:** - Pipe B has the highest rate ($0.6667$), so it is the most efficient. - Pipe A is next with $0.5$. - Pipe C is the least efficient with $0.4$. **Final answer:** Pipe B is the most efficient pipe.