The amounts x 1 (t) and x 2 (t) of salt in the two brine tanks of

Question:

The amounts x₁(t) and x₂(t) of salt in the two brine tanks of Fig. 7.3.7 satisfy the differential equations

where k_i = r/V_i for i = 1, 2. In Problems 27 and 28 the volumes V₁ and V₂ are given. First solve for x₁ (t) and x₂(1), assuming that r = 10 (gal/min), x₁ (0) = 15 (lb), and x₂ (0) = 0. Then find the maximum amount of salt ever in tank 2. Finally, construct a figure showing the graphs of x₁ (t) and x₂ (t).