To solve this problem, let’s start by analyzing the rate at which water flows through the pipes.

1. Determine the current rate of filling the pool:

   • 4 pipes can fill the swimming pool in 30 minutes.
   • This means that, collectively, 4 pipes fill $\frac{1}{30}$ of the pool per minute.

2. Calculate the rate of one pipe:

   Since all pipes have the same rate, the rate of one pipe is: $\text{Rate of one pipe} = \frac{1}{30} \div 4 = \frac{1}{120}$ So, each pipe fills $\frac{1}{120}$ of the pool per minute.

3. Adding one more pipe (total of 5 pipes):

   With 5 pipes working together, the combined rate is: $\text{Combined rate of 5 pipes} = 5 \times \frac{1}{120} = \frac{5}{120} = \frac{1}{24}$ This means that with 5 pipes, $\frac{1}{24}$ of the pool is filled per minute.

4. Calculate the time required with 5 pipes:

   Since 5 pipes fill $\frac{1}{24}$ of the pool per minute, the time to fill the pool is: $\text{Time} = \frac{1}{\text{Combined rate}} = \frac{1}{\frac{1}{24}} = 24 \text{ minutes}$

Therefore, with 5 pipes, the swimming pool would be filled in 24 minutes.

Would you like a further breakdown or have questions on any step?

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Here are 5 related questions for practice:

1. If 6 pipes are used instead of 5, how long would it take to fill the pool?
2. If the rate of each pipe is doubled, how long would it take to fill the pool with 4 pipes?
3. How many pipes would be needed to fill the pool in 15 minutes?
4. If it takes 45 minutes to fill the pool with 3 pipes, what is the filling time with 6 pipes?
5. If one of the 5 pipes breaks, how long would it take to fill the pool with the remaining 4?

Tip: When dealing with rates, remember that the total rate of work is the sum of the rates of each individual worker (or pipe, in this case).