With water from one hose, a swimming pool can be filled in 8 hours. A second, larger hose used alone can fill the pool in 4 hours. How long would it take to fill the pool if both hoses were used simultaneously?

To solve this problem, we can use the concept of combined rates of work.

### Step-by-Step Solution:

1. **Rate of the first hose**:  
   The first hose can fill the pool in 8 hours.  
   So, the rate of the first hose is \( \frac{1}{8} \) pools per hour.

2. **Rate of the second hose**:  
   The second, larger hose can fill the pool in 4 hours.  
   So, the rate of the second hose is \( \frac{1}{4} \) pools per hour.

3. **Combined rate of both hoses**:  
   When both hoses are used simultaneously, their rates add up.  
   So, the combined rate is:
   \[
   \frac{1}{8} + \frac{1}{4}
   \]
   To add these fractions, find a common denominator:
   \[
   \frac{1}{8} + \frac{2}{8} = \frac{3}{8}
   \]
   The combined rate is \( \frac{3}{8} \) pools per hour.

4. **Time to fill the pool**:  
   The time required to fill the pool is the reciprocal of the combined rate.  
   So, the time is:
   \[
   \frac{1}{\frac{3}{8}} = \frac{8}{3}
   \]
   This is approximately **2.67 hours**, or **2 hours and 40 minutes**.

### Final Answer:  
It will take approximately **2 hours and 40 minutes** to fill the pool using both hoses simultaneously.

Do you want more details on this? Also, here are 5 related questions to practice:

1. If a third hose could fill the pool in 6 hours, how long would it take to fill the pool with all three hoses?
2. What fraction of the pool would be filled by the two hoses after 1 hour?
3. How much longer would it take if only the first hose were used compared to using both hoses?
4. If both hoses were used for 1 hour, how much of the pool would still be empty?
5. If the larger hose could be used for only half the time, how long would it take to fill the pool?

**Tip**: When combining rates, always sum them before finding the total time needed.

Learn how to calculate the time required to fill a swimming pool using two hoses with different rates. This problem covers work rate concepts and combined rates, suitable for students in Grades 6-8. Includes step-by-step explanation and formulas.

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