Question

An aquarium tank can hold 5400 liters of water. There are two pipes that can be used to fill the tank. The first pipe alone can fill the tank in 90 minutes. Thesecond pipe can fill the tank in 45 minutes by itself. When both pipes are working together, how long does it take them to fill the tank?

Answer 1

30 minutes

Step-by-step explanation:

We were given the following information:

The tank can hold 5.400 liters of water

Two pipes can be used to fill the tank:

The first tank alone can fill the tank in 90 minutes

The second tank alone can fill the tank in 45 minutes

We thus have:

`\begin{gathered} First\text{ }tank: \\ velocity_(pipe1)=(5400)/(90)=60\text{ liters/minute} \\ \\ Second\text{ }tank: \\ velocity_(pipe2)=(5400)/(45)=120\text{ liters/minute} \end{gathered}`

For the combined flow of both pipes, we have:

`\begin{gathered} velocity=velocity_(pipe1)+velocity_(pipe2) \\ velocity=60+120 \\ velocity=180\text{ liters/minute} \\ \text{The time it would take to fill the tank is given by:} \\ velocity=(displacement)/(time) \\ 180=(5400)/(time) \\ \text{Cross multiply, we have:} \\ 180* time=5400 \\ time=(5400)/(180) \\ time=30minutes \\ \\ \therefore t\imaginaryI me=30m\imaginaryI nutes \end{gathered}`

Therefore, the tank will be filled in 30 minutes