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.

My work:

dq/dt=-rq/V, where r is the rate of filtration and V is the volume of the pool

dq/q=-rdt/V

lnq=-rt/V+C

at t=o, q=5000g

C=ln5000

q=5000e^(3.33E-3t)

Book Answer:

dq/dt=-q/300, q(0)=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?