Help! Got super lost in this wall of text...

Brine containing 2g of salt/L flows into a container initially filled with 50L of water containing 10g of salt. If the brine enters the tank at 5L/min, the concentration is kept uniform by stirring and the mixture flows out at the same rate. P(t) is the amount of salt (g) in the tank after t mins,. Find the amount of salt in the tank after 10 mins.

Hey! So let's start by trying to focus only on the flow of the quantity we care about, that's

**salt**. So, we know:

- 10 grams of salt flows into the tank per minute (5 litres, 2 grams per litre)

- Initially, there are 10 grams of salt in the tank

Let's look at the rate of change of salt. It is 10 grams going in per minute, and then \(\frac{P}{10}\) is flowing out per minute (5 litres out of 50 litres, one tenth of the quantity of salt in the tank at that time).

Now to find the constant C, we use the initial condition of 10 grams of salt in the tank.

So we rearrange this to get P:

And then just substitute what you need to find your answer