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To solve this problem, we need to use the concept of combined work rates. Each pipe has a certain rate at which it drains the pool, and when they work together, their combined rate will allow us to find how long it takes to drain the pool.

### Step-by-step solution:

1. **Pipe 1's rate**:
   - Pipe 1 can drain the pool in 5 days, so its rate is \( \frac{1}{5} \) of the pool per day.

2. **Pipe 2's rate**:
   - Pipe 2 can drain the pool in 7 days, so its rate is \( \frac{1}{7} \) of the pool per day.

3. **Combined rate**:
   - When both pipes work together, their combined rate is the sum of their individual rates:
   \[
   \text{Combined rate} = \frac{1}{5} + \frac{1}{7}
   \]
   To add these fractions, we find a common denominator:
   \[
   \frac{1}{5} + \frac{1}{7} = \frac{7}{35} + \frac{5}{35} = \frac{12}{35}
   \]
   So, the combined rate of both pipes is \( \frac{12}{35} \) of the pool per day.

4. **Time to drain the pool together**:
   - The time to drain the pool when both pipes are working together is the reciprocal of their combined rate:
   \[
   \text{Time} = \frac{35}{12} \text{ days}
   \]
   Simplifying this fraction gives:
   \[
   \frac{35}{12} \approx 2.92 \text{ days}
   \]

Thus, it will take approximately **2.92 days** for both pipes to drain the pool together.

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Would you like more details or have any questions?

Here are five related questions you could explore:
1. If Pipe 1 takes 4 days and Pipe 2 takes 6 days, how long will they take together?
2. How much of the pool will Pipe 1 drain in 1 day if Pipe 2 is not working?
3. If both pipes drain 50% of the pool together, how long would that take?
4. What happens if Pipe 2 is slower, taking 10 days to drain the pool?
5. How would the calculation change if there were three pipes involved?

**Tip**: When adding work rates, always express them as fractions and find a common denominator for easier calculations.

Pipe 1 takes 5 days to drain a pool and pipe 2 takes 7 days to drain the same pool. How long will it take for the two pipes to drain the pool together?

Solve the work rate problem involving two pipes. Pipe 1 takes 5 days and Pipe 2 takes 7 days to drain a pool. Learn how to calculate the combined work rate and find the total time to drain the pool when both pipes work together. Suitable for students in Grades 7-10.

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