It takes a hose 2 minutes to fill a rectangular aquarium 10 inches long, 11 inches wide, and 13 inches tall. How long will it take the same hose to fill an aquarium measuring 26 inches by 31 inches by 33 inches?
first volume = 10 * 11 * 13
second volume = 26 * 31 * 33
so
2 minutes * (26 * 31 * 33) / (10 * 31 * 33)
To find out how long it will take the hose to fill the second aquarium, we will use a concept called the ratio of volumes.
The volume of the first aquarium is given by the formula:
Volume = length * width * height = 10 inches * 11 inches * 13 inches
Similarly, the volume of the second aquarium is given by:
Volume = length * width * height = 26 inches * 31 inches * 33 inches
Now, let's calculate the ratio of volumes between the two aquariums:
Ratio of volumes = (Volume of second aquarium) / (Volume of first aquarium)
Substituting the values, we have:
Ratio of volumes = (26 inches * 31 inches * 33 inches) / (10 inches * 11 inches * 13 inches)
Calculating this ratio, we get: Ratio of volumes ≈ 8.4515
Since the ratio represents the number of times the volume of the second aquarium is greater than the first aquarium, it will also take the hose about 8.4515 times longer to fill the second aquarium.
Finally, to find out how long it will take the hose to fill the second aquarium, we multiply the original 2 minutes by the ratio:
Time to fill second aquarium = 2 minutes * 8.4515
Therefore, it will take the hose approximately 16.9 minutes to fill the aquarium measuring 26 inches by 31 inches by 33 inches.