In a swimming competition, the players were asked to swim 9 km upstream and then swim back to the point of starting. The winner of the competition could complete the task in 1 hour and 30 minutes. If the speed of the current of the river water was 8 km/hr, the speed of the winner is :
16 km/hr
20 km/hr
14 km/hr
18 km/hr
Answer is Right!
Answer is Wrong!
This question was previously asked in
UPSC CISF-AC-EXE – 2023
– Speed of the current = 8 km/hr.
– Upstream speed (against the current) = (s – 8) km/hr.
– Downstream speed (with the current) = (s + 8) km/hr.
– Distance upstream = 9 km.
– Distance downstream = 9 km.
– Total time = 1 hour 30 minutes = 1.5 hours.
– Time upstream = Distance / Upstream speed = 9 / (s – 8) hours.
– Time downstream = Distance / Downstream speed = 9 / (s + 8) hours.
– Total time equation: 9/(s – 8) + 9/(s + 8) = 1.5
– Multiply the equation by (s – 8)(s + 8): 9(s + 8) + 9(s – 8) = 1.5(s – 8)(s + 8)
– 9s + 72 + 9s – 72 = 1.5(s² – 64)
– 18s = 1.5s² – 96
– Multiply by 2: 36s = 3s² – 192
– Divide by 3: 12s = s² – 64
– Rearrange into a quadratic equation: s² – 12s – 64 = 0
– Factor the equation: (s – 16)(s + 4) = 0
– Possible values for s are 16 or -4. Since speed must be positive, s = 16 km/hr.
– The speed of the swimmer (16 km/hr) must be greater than the speed of the current (8 km/hr) for upstream movement to be possible, which is true (16 > 8).