Question

it takes a hose 4 minutes to fill a rectangular aquarium 8 inches long, 9 inches wide, and 11 inches tall. how long will it take the same hose to fill an aquarium measuring 22 inches by 24 inches by 31 inches?
minutes
round your answer to the nearest minute
question help: video message instructor

Explanation:

Step1: Calculate volume of first aquarium

The volume \( V_1 \) of a rectangular prism is \( V = l \times w \times h \). For the first aquarium, \( l = 8 \), \( w = 9 \), \( h = 11 \). So \( V_1 = 8\times9\times11 = 792 \) cubic inches.

Step2: Calculate volume of second aquarium

For the second aquarium, \( l = 22 \), \( w = 24 \), \( h = 31 \). So \( V_2 = 22\times24\times31 = 22\times744 = 16368 \) cubic inches.

Step3: Find the rate of filling

The rate \( r \) is volume per time. The first aquarium takes 4 minutes, so \( r=\frac{V_1}{4}=\frac{792}{4} = 198 \) cubic inches per minute.

Step4: Calculate time for second aquarium

Time \( t \) for second aquarium is \( t=\frac{V_2}{r}=\frac{16368}{198}=82.66\cdots\approx83 \) minutes.

Answer:

83