A rectangular swimming pool has a length of 30 meters, a width of 10 meters, and an average depth of 2 meters. If a hose can fill the pool at a rate of 0.5 cubic meters per minute, how many hours will it take the hose to fill the pool?

Answer

To solve the problem step by step, let's follow the outlined process:

### Step 1: Calculate the volume of the swimming pool
The volume \( V \) of a rectangular swimming pool can be calculated using the formula:
\[ V = \text{length} \times \text{width} \times \text{depth} \]
Given:
- Length = 30 meters
- Width = 10 meters
- Depth = 2 meters

Substituting the values into the formula:
\[ V = 30 \, \text{m} \times 10 \, \text{m} \times 2 \, \text{m} = 600 \, \text{cubic meters} \]

### Step 2: Determine the rate at which the hose fills the pool
The hose fills the pool at a rate of:
\[ \text{Rate} = 0.5 \, \text{cubic meters per minute} \]

### Step 3: Calculate the time taken to fill the pool in minutes
To find the total time \( T \) in minutes to fill the pool, we use the formula:
\[ T = \frac{\text{Volume of the pool}}{\text{Rate of filling}} \]
Substituting the known values:
\[ T = \frac{600 \, \text{cubic meters}}{0.5 \, \text{cubic meters per minute}} = 1200 \, \text{minutes} \]

### Step 4: Convert the time from minutes to hours
To convert minutes into hours, we use the conversion:
\[ \text{Hours} = \frac{\text{Minutes}}{60} \]
Substituting the value we calculated:
\[ \text{Hours} = \frac{1200 \, \text{minutes}}{60} = 20 \, \text{hours} \]

### Final Answer
It will take the hose **20 hours** to fill the swimming pool.

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