An inlet pipe can fill a pool in 13 hours, while and outlet pipe can empty a pool in 14 hours. If both pipes are open, how long will it take to fill the pool?
The correct answer and explanation is:
✅ Correct Answer:
182 hours
🧠 Explanation:
To solve this problem, we analyze the rates at which the inlet and outlet pipes work and combine them to find the net rate when both are open.
Step-by-step Breakdown:
1. Determine the Rate of Each Pipe
- Inlet pipe fills 1 pool in 13 hours
➤ So, its rate is: Inlet rate=113 pool per hour\text{Inlet rate} = \frac{1}{13} \text{ pool per hour} - Outlet pipe empties 1 pool in 14 hours
➤ So, its rate is: Outlet rate=−114 pool per hour\text{Outlet rate} = -\frac{1}{14} \text{ pool per hour} (Negative sign indicates it’s draining water.)
2. Find the Net Rate When Both Are Open
Net rate=113−114\text{Net rate} = \frac{1}{13} – \frac{1}{14}
To subtract these, find the least common denominator: 113−114=14−13182=1182\frac{1}{13} – \frac{1}{14} = \frac{14 – 13}{182} = \frac{1}{182}
3. Time to Fill the Pool
If the net rate is 1182\frac{1}{182} pools per hour, then: Time=1Net rate=11182=182 hours\text{Time} = \frac{1}{\text{Net rate}} = \frac{1}{\frac{1}{182}} = 182 \text{ hours}
💡 Interpretation:
When both pipes are open:
- The inlet is filling the pool, but
- The outlet is removing some water.
- The net effect is very slow filling — only 1/182 of the pool per hour.
Thus, it will take 182 hours to completely fill the pool with both pipes open.
This problem emphasizes understanding opposing rates and combining them algebraically.