Question

A small lake, which is initially clean and has an initial volume of 40,000 cubic meters, has two creeks flowing into it (creek A and creek B) and one creek flowing out (creek C). Each day, 800 cubic meters of water flow into the lake from creek A, 200 cubic meters per day flow into the lake from creek B, and 1000 cubic meters flow out of the lake via creek C. At time t = 0, the water flowing into the lake from creek A becomes contaminated with road salt at a concentration of 10 kilograms per 400 cubic meters. Suppose that the water in the lake is well mixed so the concentration of salt at any given time is constant. To complicate the matter, suppose also that at time t = 0, someone begins dumping trash into the lake at a rate of 50 cubic meters per day, which settles to the bottom of the lake, reducing the volume by 50 cubic meters per day. To adjust for the incoming trash, the rate that water flows out via creek C increases to 1050 cubic meters per day and the banks of the lake do not overflow. Find the amount of salt in the lake at time t, where t is in days.

Answer 1