Step 1 :Convert the dosage from mg to g: \(600 mg = 0.6 g\)
Step 2 :Find out how many cm³ of the solution contains the required dosage: \(0.6 g / 0.043333333333333335 g/cm³ = 13.846153846153845 cm³\)
Step 3 :Convert the time from minutes to hours: \(240 minutes = 4.0 hours\)
Step 4 :Calculate the pump rate by dividing the volume of the solution by the time in hours: \(13.846153846153845 cm³ / 4.0 hours = 3.4615384615384612 cm³/hour\)
Step 5 :Round the pump rate to the nearest cubic centimeter: \(round(3.4615384615384612) = 3\)
Step 6 :Final Answer: The pump should be set at a rate of \(\boxed{3}\) cc per hour.