The concentration of pollutants in a certain river is increasing at the rate of 150 ppm (parts per million) per hour. In addition, the pollution concentration increases with distance in the direction of the river flow due to an influx from sewer lines. This latter rate of increase can be expressed as 50 ppm/mi at a certain point in the river. The river flows at 5 mi/h.

(a) A boat is used to survey the pollution concentration. Find the apparent rates of pollution concentration (in parts per million per hour) if the boat is headed upstream or downstream and cruises at 8 mi/h relative to the water. Repeat for the case where the boat is just drifting with the current.

(b) Which, if any, of the above results corresponds to the derivative moving with the flow, given by D(pollution)/Dt?