It takes a hose 5 minutes to fill a rectangular aquarium 9 inches long, 11 inches wide, and 12 inches tall. How long will it take the same hose to fill an aquarium measuring 31 inches by 32 inches by 33 inches?

minutes

9 * 11 * 12 = 1,188 cubic inches

31 * 32 * 33 = 32,736 cubic inches

5/1,188 = x/32,736

Cross multiply and solve for x.

137.77778

To find out how long it will take to fill the second aquarium, we need to compare the volume of the two aquariums.

The volume of the first aquarium is calculated by multiplying the length (9 inches), width (11 inches), and height (12 inches):

Volume1 = 9 inches * 11 inches * 12 inches

The volume of the second aquarium is calculated in the same way, using the dimensions given:

Volume2 = 31 inches * 32 inches * 33 inches

Now, we can calculate the ratio of the two volumes.

Ratio = Volume2 / Volume1

Next, we need to determine how long it takes to fill the first aquarium. We know it takes 5 minutes.

Finally, we can calculate how long it will take to fill the second aquarium by multiplying the ratio by the time it takes to fill the first aquarium.

Time to fill second aquarium = Ratio * Time to fill first aquarium = Ratio * 5 minutes

Let's calculate the values to find the answer.

To determine how long it will take for the same hose to fill the larger aquarium, we can use the principle of similar shapes. Since the two aquariums are similar, their dimensions are in proportion with each other.

To find the ratio of the two aquariums, we compare their lengths, widths, and heights:

Length ratio: 31 inches / 9 inches = 3.44 (rounded to two decimal places)
Width ratio: 32 inches / 11 inches = 2.91 (rounded to two decimal places)
Height ratio: 33 inches / 12 inches = 2.75 (rounded to two decimal places)

Since the dimensions are proportional, we can assume that the volume of the larger aquarium is equal to the volume of the smaller aquarium multiplied by the ratios of each side:

Volume ratio = Length ratio x Width ratio x Height ratio

Volume ratio = 3.44 x 2.91 x 2.75 = 26.54 (rounded to two decimal places)

Therefore, the volume of the larger aquarium is approximately 26.54 times the volume of the smaller aquarium.

Given that it takes 5 minutes to fill the smaller aquarium, we can infer that it will take approximately 5 minutes x 26.54 = 132.7 minutes to fill the larger aquarium.

Therefore, it will take approximately 132.7 minutes to fill the larger aquarium with the same hose.