Question

An aquarium tank can hold 6300 liters of water. There are two pipes that can be used to fill the tank.The first pipe alone can fill the tank in 84 minutes. The second pipe can fill the tank in 42 minutes by itself. When both pipes are working together, how long does it take them to fill the tank?

Answer 1

Answer: it will take them 28 minutes to fill the tank.

Step-by-step explanation:

The first pipe alone can fill the tank in 84 minutes. This means that the rate at which the first pipe fills the tank per minute is 1/84

The second pipe can fill the tank in 42 minutes by itself. This means that the rate at which the second pipe fills the tank per minute is 1/42

If they work together, they would work simultaneously and their individual rates are additive. This means that their combined rate of filling the tank would be

1/84 + 1/42

Assuming it takes t hours for both pipes to fill the tank working together, the working rate per minute would be 1/t. Therefore,

1/84 + 1/42 = 1/t

3/84 = 1/t

t = 84/3

t = 28 minutes

Answer 2

Answer:

28 minutes

Step-by-step explanation:

The aquarium tank can hold 6300 litres of water.

First pipe can fill the tank in 84 minutes.

So in 1 minute it fills $\[\frac{6300}{84}\]$ litres of water.

That is, in 1 minute it fills $\[75\]$ litres of water.

Second pipe can fill the tank in 42 minutes.

So in 1 minute it fills $\[\frac{6300}{42}\]$ litres of water.

That is, in 1 minute it fills $\[150\]$ litres of water.

When the two pipes are working together they are adding $\[75+ 150 = 225\]$ litres of water per minutes to the tank.

So to fill the tank of capacity 6300 litre it will take $\[\frac{6300}{225}\]$ minutes.

In other words, it will take 28 minutes to fill the complete tank.