It takes a hose 4 minutes to fill a rectangular aquarium 8 inches long, 9 inches wide, and 10 inches tall. How long will it take the same hose to fill an aquarium measuring 22 inches by 26 inches by 34 inches?
(22*26*34)/(8*9*10) * 4 ≈ 108 minutes
To find the time it takes to fill the second aquarium, we need to compare the volume of the two aquariums and determine the ratio of their fill times.
First, let's find the volume of the first aquarium:
Volume = length × width × height
Volume = 8 inches × 9 inches × 10 inches
Volume = 720 cubic inches
We know that it took 4 minutes to fill the first aquarium. Therefore, the flow rate of the hose can be calculated as:
Flow rate = Volume / Time
Flow rate = 720 cubic inches / 4 minutes
Flow rate = 180 cubic inches per minute
Now, we can calculate the fill time for the second aquarium using the flow rate we just found:
Fill time = Volume / Flow rate
Fill time = (22 inches × 26 inches × 34 inches) / 180 cubic inches per minute
To calculate this, we need to convert the dimensions of the second aquarium to inches:
22 inches = 22 inches
26 inches = 26 inches
34 inches = 34 inches
Fill time = (22 inches × 26 inches × 34 inches) / 180 cubic inches per minute
Fill time = 19,324 cubic inches / 180 cubic inches per minute
Fill time ≈ 107.36 minutes
So, it will take approximately 107.36 minutes (or about 1 hour and 47 minutes) for the same hose to fill an aquarium measuring 22 inches by 26 inches by 34 inches.