Consider there are two rain gauges (A and B) in a watershed with an area of 21.6 km2. The cumulative rainfall depths over time for a particular storm event at both rain gauge stations are given in the table below. The storm also produces a runoff hydrograph at the outlet of the watershed, shown in the last row of the table. Assume that the baseflow is 10 m3/s. It is known, by the Thiessen polygon, that the contributing areas for the rain gauges are identical Time (hr) Cumul. Rainfall at Station A (mm) Cumul. rainfall at Station B (mm) Instantaneous discharge (m/s) 0 1 2 3 4 5 6 7 0 25 80 105 100 140 180 230 230 8 9 10 0 15 40 85 130 180 210 230 230 10 10 30 60 30 40 80 40 30 10 10 (a) Determine the basin-wide representative rainfall hyetograph (in mm/hr) for the storm event. Furthermore, determine the value of f index (in mm/hr) and the corresponding effective rainfall hyetograph (in mm/hr). (b) Set up the system of equations Pu % Q. (c) Solve part (b) by the least-squares method for the unit hydrograph. What is the duration of the unit hydrograph obtained?