29) a tank contains 100 gallons of water in which 40 pounds of salt are dissolved. it isdesired to reduce the concentration of salt to 0.1 pounds per gallon by pouring in purewater at the rate of 5 gallons per minute and allowing the mixture (which is kept uniformby stirring) to flow out at the same rate. how long will this take

The amount of salt in the tank at time , denoted by , changes over time according to the differential equation,

Multiply both sides by :

Now the left side can be condensed to the derivative of a product:

Integrate both sides to get

and solving for gives

Given that there are 40 pounds of salt at the start, or , we know , so that

We want the concentration to fall to 0.1 lb/gal, which means

so it would take about 73.78 minutes, or about 1.23 hours, for the concentration to fall to 0.1 lb/gal.

341

step-by-step explanation:

all you have to do is 9x31 (which equals 279) and then 20x31 (which equals 620). then you have to subtract. 620-279=341.