Question

It takes a hose 4 minutes to fill a rectangular aquarium 10 inches long, 11 inches wide, and 12 inches tall. How long will it take the same hose to fill an aquarium measuring 30 inches by 33 inches by 35 inches?

Answer 1

First, let's find the flow rate, it will be

`Q=(\Delta V)/(\Delta t)`

Where ΔV = 10*11*12, and Δt = 4 minutes, therefore

`Q=(\Delta V)/(\Delta t)=(10\cdot11\cdot12)/(4)=(1320)/(4)=330\text{ ft}^3/\text{ min}`

Now we can use the same definition and solve it for Δt

`Δt=(\Delta V)/(Q)`

But now we use the new volume and the previous flow rate

`Δt=(\Delta V)/(Q)=(30\cdot33\cdot35)/(330)=105\text{ minutes}`

Therefore it will take 105 minutes.