Differential Equations help

Hey, I'm completely stuck on where to start on this question. Any hints?

A tank contains a perfectly mixed solution of 5kg of salt and 500 litres of water. Starting at t=0, fresh water is poured into the tank at a rate of 4 litres/min. A mixing device maintains homogeneity. The solution leaves the tank at a rate of 4 litres/min.

a) What is the differential equation governing the amount of salt in the tank at any time?
b) In how many minutes will the concentration of salt reach a 0.1% level (i.e. initial concentration is 1%)

Note that for full marks you need to explain your working, not just write down the final answers.

Reply 1

ghostwalker

17

Original post by Jimbojambo

a) What is the differential equation governing the amount of salt in the tank at any time?

Does this not suggest a variable to use?

Then what's 4 l/min in terms of the amount of salt?

See what you can do with that.

Reply 2

TeeEm

19

Original post by Jimbojambo

Hey, I'm completely stuck on where to start on this question. Any hints?

A tank contains a perfectly mixed solution of 5kg of salt and 500 litres of water. Starting at t=0, fresh water is poured into the tank at a rate of 4 litres/min. A mixing device maintains homogeneity. The solution leaves the tank at a rate of 4 litres/min.

a) What is the differential equation governing the amount of salt in the tank at any time?
b) In how many minutes will the concentration of salt reach a 0.1% level (i.e. initial concentration is 1%)

Note that for full marks you need to explain your working, not just write down the final answers.

look at the link

http://madasmaths.com/archive_maths_booklets_standard_topics_integration.html

download PDF: odes_context_modelling
(NOTE THAT IT TAKES AGES TO DOWNLOAD DUE TO SIZE)

There is a very similar question in page 75

Look at how the question is attempted

you may adapt it to your ODE