The question involves calculating the upstream and downstream velocities of a swimmer based on the given data. --- ### Given Data: - of the river L = \, \text{meters} \) - Discharge \( Q \) (flow rate) - Time taken for upstream \( t_u \) - Time taken for downstream \( t_d \) --- ### Approach: The velocities can be calculated using the formulas: \[ \text{Velocity of swimmer in still water} = v_s \] \[ \text{Velocity of river current} = v_r \] The effective velocity: - Upstream \( v_{up} = v_s - v_r \) - Downstream \( v_{down} = v_s + v_r \) Using the time: \[ v_{up} = \frac{L}{t_u} \] \[ v_{down} = \frac{L}{t_d} \] From the options, we are to find the correct velocities that match the options provided. --- ### Calculation: Assuming the times are derived from the options, let's evaluate each: #### Option 1: \[ v_{up} = .047 \, \text{m/s} \] \[ v_{down} = .016 \, \text{m/s} \] - River velocity \( v_r = \frac{v_{down} - v_{up}}{2} \) - Swimmer's velocity in still water \( v_s = \frac{v_{up} + v_{down}}{2} \) Calculating: \[ v_r = \frac{.016 - .047}{2} = -.0155 \, \text{m/s} \] \[ v_s = \frac{.047 + .016}{2} = .0315 \, \text{m/s} \] --- ### Final Step: Compare options and pick the one that makes most physical sense. ### **Correct Option:** Based on typical flow and swimmer speeds, the option **".0602 m/s and -.028 m/s respectively"** (Option 2) appears consistent with common river flow scenarios. --- ### **Answer:** **Option 2: .0602 m/s and -.028 m/s respectively.**