Suppose there are two lakes located on a stream. Clean water flows into the first lake, then the water from the first lake flows into the second lake, and then water from the second lake flows further downstream. The in and out flow from each lake is 500 litres per hour. The first lake contains 100,000 litres of water and the second lake contains 200,000 litres of water. A truck with 500 kg of toxic substance crashes into the first lake. Assume that the water is being continually mixed perfectly by the stream. See DiffyQs 1.4.9.

(a) Let M1(t) and M2(t) be respectively the mass of toxic substance (in kg) in the first and second lake as a function of time t (in hours). Find the differential equations satisfied by M1(t) and M2(t). Justify your answer.

(b) Find M1(t). (c) Find M2(t).