Tank t_1 initially contain 50 gallons of pure water. starting at t_0 = 0, water that contains 1 pound of salt per gallon is poured into t_1 at the rate of 2 gal/min. the mixture is drained from t_1 at the same rate into a second tank t_2, which initially contains 50 gallons of pure water. also starting at t_0 = 0, a mixture from another source that contains 2 pounds of salt per gallon is poured into t_2 at the rate of 2 gal/min. the mixture is drained from t_2 at the rate of 4 gal/min. a) find a differential equation for the quantity q(t) of salt in tank t_2 at time t > 0. b) solve the equation derived in (a) to determine q(t). c) find lim_t rightarrow infinity q(t).