It takes a hose 4 minutes to fill a rectangular aquarium 8 inches long, 9 inches wide, and 14 inches tall. How long will it take the same hose to fill an aquarium measuring 24 inches by 27 inches by 31 inches?
To solve this problem, we need to find the volume of each aquarium and then compare the ratios of their volumes to determine how long it will take to fill the second aquarium.
1. Calculate the volume of the first aquarium:
Volume = length × width × height
Volume = 8 inches × 9 inches × 14 inches
Volume = 1008 cubic inches
2. Calculate the volume of the second aquarium:
Volume = length × width × height
Volume = 24 inches × 27 inches × 31 inches
Volume = 19944 cubic inches
3. Find the ratio of the volume of the second aquarium to the first aquarium:
Ratio = Volume of the second aquarium / Volume of the first aquarium
Ratio = 19944 cubic inches / 1008 cubic inches
Ratio = 19.75
4. Since the ratio represents how many times larger the second aquarium is compared to the first, the same ratio can be applied to find the time it takes to fill the second aquarium:
Time for the second aquarium = ratio × time for the first aquarium
Time for the second aquarium = 19.75 × 4 minutes
Time for the second aquarium = 79 minutes
Therefore, it will take the same hose approximately 79 minutes to fill the second aquarium measuring 24 inches by 27 inches by 31 inches.
To solve this problem, we can use the concept of ratios.
First, let's find the volume of the first aquarium. The volume of a rectangular aquarium is calculated by multiplying its length, width, and height. For the first aquarium, the volume is given by 8 inches * 9 inches * 14 inches = 1,008 cubic inches.
Now, let's calculate the volume of the second aquarium. The volume of the second aquarium is given by 24 inches * 27 inches * 31 inches = 19,368 cubic inches.
We can set up a ratio using the volumes of the two aquariums:
1,008 cubic inches / 4 minutes = 19,368 cubic inches / x minutes
To find the time it takes to fill the second aquarium, x, we need to solve for x in the above equation.
By cross-multiplying and solving the equation, we get:
1,008 * x = 19,368 * 4
Now, we can solve for x by dividing both sides of the equation by 1,008:
x = (19,368 * 4) / 1,008
Calculating this expression, we find:
x = 77,472 / 1,008
x ≈ 76.79
Therefore, it would take approximately 76.79 minutes for the same hose to fill the aquarium measuring 24 inches by 27 inches by 31 inches.
It takes a hose 4 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 24 inches by 26 inches by 32 inches?
8 times 9 times 14 =1008
24 times 27 times 31 =19440
4/1008 = x/19440
77.14 minutes