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Q2 (CISF/2023) Science & Technology › Basic Science (Physics, Chemistry, Biology)

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 :

Explanation

Let the speed of the swimmer in still water be u km/hr and the speed of the river current be v = 8 km/hr.

  • Upstream speed = u - v = (u - 8) km/hr
  • Downstream speed = u + v = (u + 8) km/hr

The total distance is 9 km each way, and the total time taken is 1 hour 30 minutes, which is 1.5 hours (or 3⁄2 hours). Using the formula Time = Distance / Speed:

9 / (u - 8) + 9 / (u + 8) = 1.5

Multiplying the entire equation by (u - 8)(u + 8):
9(u + 8) + 9(u - 8) = 1.5(u2 - 64)
18u = 1.5(u2 - 64)
12u = u2 - 64
u2 - 12u - 64 = 0

Factoring the quadratic equation: (u - 16)(u + 4) = 0. Since speed cannot be negative, u = 16 km/hr.

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