00:01
So for this problem, we have a 50 -gallon tank initially containing 10 gallons of fresh water.
00:05
Time equals zero has a pound of salt per gallon.
00:12
So we know that we want to find d .p.
00:15
D .t.
00:17
Which is the rate in minus the rate out.
00:20
Well, the rate in is going to be four minus whatever the p value is coming in over.
00:39
5 plus.
00:42
We know that because we have, it's entering the tank at four gallons per minute, and then the brine solution, it's going to be one pound of salt per gallon.
00:57
And then we know that it's leaving at a rate.
01:03
So this is, the rate's coming in is 4 over 10 plus 2t, because that's the initial 10 gallons of water and then we have one pound of salt per gallon poured into the tank at four gallons per minute.
01:23
So with that we know that what's leaving is going to be p the amount of salt over 5 plus t because we know the well -stir mixture is leaving the rate of the tank at two gallons per minute.
01:43
So in this case what we're going to have is subtracting these, we have 4 minus p over 5 plus t, because this was 10 plus 2t, then we multiply it by 2 because that's the rate at which it's leaving.
02:09
So then initially time equals 0, we see no salt in the tank...