Math Is Fun Forum

Icy950

Member

Registered: 2007-06-11

Posts: 1

Need help with DEs problems

Hello
I'm taking 256Mth, I have many homework problems like the below one.
Any1 plz help me solve this problem? So I can have some kind of idea to solve the rest.
Thanks a lot

A large tank is partically filled with 100 gal of fliud in which 10 lbs of salt is dissolved. Brine containing 1/2 lb of salt per gallon is pumped into the tank at a rate of 6 gal/min. The well-mixed solution is then pumped out at a slower rate of 4 gal/min.  Find the number of pounds of salt in the tank after 25 mins.

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: Need help with DEs problems

This is a calculus problem I think, but to set it up, I would computer program an estimate, by breaking the time smaller and smaller for better estimates.  You can alternate filling and draining in tiny time intervals, even though it happens all at once.   At least it might be close.
For example, if you use large time intervals for a rough estimate, and go by minutes, then the first minute is broken into two pretend fill and empty minutes, where 13 lbs would of 106 is salt, then drain it and 13 * 102 / 106 would remain, or about 12.9, just guessing after first minute.
When you figure this out, let us know sort of how, it's very interesting.

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igloo myrtilles fourmis

Old_Steve

Member

Registered: 2007-05-15

Posts: 17

Re: Need help with DEs problems

Let C(t) = Salt concentration at any time t.
Let Q(t) = Amount of salt in the tank at time t.
C(t) = Q(t)/100
dQ/dt at which Q(t) changes is equal to rate in minus rate out.  Rate in is 1/2 * 6 = 3lbs/min
Rate out is teh concentration out * rate drained.  C(t)lbs/min * 4 gal/min

p(x)= 0.04 and g(x) = 0.03

At zero time C(0) = 10lbs/100gal = .1

solve

Hopefully, this will get you the right equation to plug in your time for t - 25min