Please help me solve this problem just need the answer~! (1 Viewer)

[Boonyak]

Q: A water tank contains 500L of salty water with salt concentration 20grams per litre, fresh water with a salt concentration of 2 grams per litre flows into the tank at a rate of 8 litres per minute. The concentration of salt in the tank is kept constant by stirring and the resulting mixture flows out of the tank at a rate of 8 litres per minute.

Find when (in minutes to two decimal places) the concentration of the mixture in the tank is 5 grams per litre.​

 

[Sy123]

Just clarifying, so initially there is 500L of salty water in the tank with 20g/L salt concentration. And fresh water 2g/L salt is flowing into the tank at 8L/min?

If so I will start solving it

 

[Boonyak]

I think so and it says "The concentration of salt in the tank is kept constant by stirring and the resulting mixture flows out of the tank at a rate of 8 litres per minute."

 

[fortune_cookie]

This question is a first year university question. It involves deriving a differential equation (which I am fairly sure is linear) and then solving it.

This is definately not 2 unit level difficulty.

 

[iSplicer]

This question is a first year university question. It involves deriving a differential equation (which I am fairly sure is linear) and then solving it.

This is definately not 2 unit level difficulty.

Pretty sure I've seen it in Extension 1...

There's a nice example in Pender's Cambridge, and Fitzy iirc.

 

[Boonyak]

Yea i know its for a friend didnt know were to put it

 

[Sy123]

:| Ive been trying for about 15 mins at a question I cant solve.
Ah well, it was fun trying

 

[fortune_cookie]

See this video for the general method for these questions: http://www.youtube.com/watch?v=0I020topCv0&list=PL0B78D947E5714F4D&index=11&feature=plpp_video


Once again, I will stress that this sort of question will definately not be asked in a 2 unit mathematics paper. It could possibly show in the later questions of a 3 unit paper , or a 4 unit paper. But definately not a 2 unit paper. It involves solving a linear differential equation.

I guess they could just ask you to set up the differential equation and not physically solve it. Something like "show dy/dt = .........." but it is pretty unlikely.