It takes a hose 5 minutes to fill a rectangular aquarium 8 inches long, 13 inches wide, and 14 inches tall. How long will it take the same hose to fill an aquarium measuring 21 inches by 34 inches by 35 inches?

To solve this problem, we need to determine the volumes of both aquariums and then use the relationship between their volumes to calculate the time required to fill the larger aquarium.

### Step 1: Calculate the volume of the smaller aquarium.
The dimensions of the smaller aquarium are 8 inches long, 13 inches wide, and 14 inches tall.

\[
\text{Volume of the smaller aquarium} = 8 \times 13 \times 14 = 1456 \text{ cubic inches}
\]

### Step 2: Calculate the volume of the larger aquarium.
The dimensions of the larger aquarium are 21 inches long, 34 inches wide, and 35 inches tall.

\[
\text{Volume of the larger aquarium} = 21 \times 34 \times 35 = 24990 \text{ cubic inches}
\]

### Step 3: Determine the time ratio based on the volumes.
The time it takes to fill the aquarium is proportional to the volume, so we can set up a ratio comparing the two volumes and their corresponding times.

Let \( t \) be the time to fill the larger aquarium.

\[
\frac{t}{5} = \frac{\text{Volume of the larger aquarium}}{\text{Volume of the smaller aquarium}} = \frac{24990}{1456}
\]

\[
t = 5 \times \frac{24990}{1456} \approx 85.8 \text{ minutes}
\]

### Final Answer:
It will take approximately **85.8 minutes** (or about 1 hour and 26 minutes) to fill the larger aquarium with the same hose.

Would you like more details or have any questions?

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Here are 5 related questions:
1. How would the time change if the water flow rate from the hose were doubled?
2. What if the larger aquarium was only half filled—how long would that take?
3. How does the volume of different geometric shapes compare, like a cylinder or sphere?
4. How could you calculate the time if the hose had varying flow rates?
5. What factors might affect the actual time it takes to fill an aquarium, such as water pressure?

**Tip:** Understanding the relationship between volume and time is crucial for tasks involving fluid dynamics, whether filling containers or planning water distribution systems.

Learn how to calculate the time required to fill rectangular aquariums using fluid dynamics principles. Solve a specific problem involving volumes and flow rates of hoses. Suitable for students in Grades 7-9.

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