A pool of 60,000 gal water is contaminated with 5kg of dye. The filter can remove the dye and pumps at a rate of 200 gal/min find the initial value problem. let q(t) be the amount of dye in the pool at any time t.
dq/dt=-rq/V, where r is the rate of filtration and V is the volume of the pool
at t=o, q=5000g
The rate of filtration is being taken out of the volume of the pool. Why would the book choose to use the ratio -V/r?