It takes a hose 4 minutes to fill a rectangular aquarium 9 inches long, 10 inches wide, and 14 inches tall. How long will it take the same hose to fill an aquarium measuring 21 inches by 22 inches by 26 inches?


To determine how long it will take the same hose to fill a larger aquarium, we can use the fact that the time required is proportional to the volume of the aquarium.

### Step 1: Calculate the Volume of Both Aquariums

- **Original aquarium volume**:  
  \[
  9 \text{ inches} \times 10 \text{ inches} \times 14 \text{ inches} = 1260 \text{ cubic inches}
  \]

- **New aquarium volume**:  
  \[
  21 \text{ inches} \times 22 \text{ inches} \times 26 \text{ inches} = 12012 \text{ cubic inches}
  \]

### Step 2: Set Up the Proportion

The time required to fill the aquarium is proportional to the volume:

\[
\frac{\text{Time for original aquarium}}{\text{Volume of original aquarium}} = \frac{\text{Time for new aquarium}}{\text{Volume of new aquarium}}
\]

\[
\frac{4 \text{ minutes}}{1260 \text{ cubic inches}} = \frac{T \text{ minutes}}{12012 \text{ cubic inches}}
\]

### Step 3: Solve for the Time \( T \)

\[
T = \frac{4 \times 12012}{1260}
\]

\[
T = \frac{48048}{1260} \approx 38.14 \text{ minutes}
\]

### Final Estimate:
It will take approximately **38.14 minutes** to fill the larger aquarium.

Would you like more details or have any questions?

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Here are some related questions you might find useful:
1. How does the shape of the container affect the filling time?
2. What other factors could influence the filling time aside from volume?
3. How would the time change if the hose had a different flow rate?
4. Can this proportional relationship be used for other types of fluid containers?
5. How can we calculate the flow rate of the hose based on this information?

**Tip:** When working with proportional relationships, it's important to remember that both sides of the equation should represent equivalent units and types of measurements.

Learn how to calculate the time it takes to fill an aquarium using proportional relationships and volume calculations. This problem involves determining the filling time for two rectangular aquariums based on their volumes. Suitable for Grades 7-9 students and anyone interested in mathematical applications.

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