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.
Pipe Efficiency
Step-by-step solutions with LaTeX - clean, fast, and student-friendly.