Problem 1 (15 pts) The water temperature in a river downstream of an electric power station decreases with time and distance from the plant as T(x, t), where t is time and x is the distance downstream from the plant. The speed of the current in the river is v(x). i) What is the time rate of change of temperature of the river as perceived from a fixed position x on the shoreline at time ti? ii) What is the time rate of change of temperature of the river as perceived by a boater floating with the current, at position xi and time t? iii) What is the time rate of change of temperature of the river as perceived by a boater who paddles at a steady velocity vp relative to the river, in the direction of the current, at position Xi and time t