It takes a hose 2 minutes to fill a rectangular aquarium 8 inches long, 9 inches wide, and 11 inches tall. How long will it take the same hose to fill an aquarium measuring 27 inches by 29 inches by 32 inches?

First, let's solve the problem step by step by comparing the volumes of the two aquariums.

### Step 1: Calculate the volume of the smaller aquarium
The formula for the volume of a rectangular aquarium is:

\[
V = \text{length} \times \text{width} \times \text{height}
\]

For the smaller aquarium:

\[
V_{\text{small}} = 8 \times 9 \times 11 = 792 \, \text{cubic inches}
\]

### Step 2: Calculate the volume of the larger aquarium
For the larger aquarium:

\[
V_{\text{large}} = 27 \times 29 \times 32 = 25,056 \, \text{cubic inches}
\]

### Step 3: Set up the ratio of volumes
The time it takes to fill the aquariums depends on their volumes. The time for the larger aquarium will be proportional to the volume ratio.

\[
\frac{\text{time for large aquarium}}{\text{time for small aquarium}} = \frac{V_{\text{large}}}{V_{\text{small}}}
\]

\[
\frac{t_{\text{large}}}{2} = \frac{25,056}{792}
\]

\[
t_{\text{large}} = 2 \times \frac{25,056}{792} = 2 \times 31.64 \approx 63.28 \, \text{minutes}
\]

### Answer:
It will take approximately **63.28 minutes** (or about 1 hour and 3 minutes) to fill the larger aquarium.

Do you want more details on this? Here are some related questions to consider:

1. How would the time change if the dimensions of the larger aquarium were doubled?
2. What is the flow rate of the hose in cubic inches per minute?
3. How would you convert the volumes from cubic inches to gallons?
4. How long would it take to fill the small aquarium if the hose were twice as fast?
5. How does the shape of the aquarium affect the fill time if the volume remains constant?

**Tip**: When dealing with proportional relationships, it's often useful to find the ratio of the variables you're comparing to quickly scale up or down.

Solve a practical problem using volume ratios: Learn how to calculate the time it takes to fill a larger aquarium based on the dimensions of a smaller tank. This example involves proportionality, geometry, and volume calculation concepts, suitable for students in Grades 6-8.

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