It takes a hose 3 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 22 inches by 25 inches by 26 inches?
10 * 11 * 13 = 1430 cubic inches
22 * 25 * 26 = 14,300 cubic inches
1430/3 = 476.666 cubic inches per minute
476.6667/1 = 14,300/x
Cross multiply and solve for x.
To find the time it takes to fill the second aquarium, we can use the concept of ratios and proportions.
First, let's calculate the volume of the first aquarium. The volume of a rectangular prism is calculated by multiplying its length, width, and height:
Volume of the first aquarium = 10 inches * 11 inches * 13 inches = 1,430 cubic inches
Now, we can set up a proportion to find the time it takes to fill the second aquarium. Since the volume of the first aquarium is known, we can set up the following ratio:
(Time to fill first aquarium)/(Volume of first aquarium) = (Time to fill second aquarium)/(Volume of second aquarium)
Plugging in the values, we have:
3 minutes / 1,430 cubic inches = (Time to fill second aquarium) / (22 inches * 25 inches * 26 inches)
Now, let's solve for the time to fill the second aquarium.
(Time to fill second aquarium) = (3 minutes * (22 inches * 25 inches * 26 inches)) / (1,430 cubic inches)
Calculating this expression:
(Time to fill second aquarium) = (3 minutes * 14,300 cubic inches) / (1,430 cubic inches)
Simplifying:
(Time to fill second aquarium) = 30 minutes
Therefore, it will take the same hose 30 minutes to fill an aquarium measuring 22 inches by 25 inches by 26 inches.