So who wins??

• Total time for swimming up and downstream:

T1 = ?2 (2w/s)

• Total time for swimming across stream and back:

T2 = ? (2w/s)

• Which time is smaller?

  Take ratio: T1 / T2 = ?
  
  For race to be possible, s > v
  ? ? = 1 / sqrt(1 - (v/s) 2 )) > 1

• Therefore, swimmer going across stream and back wins!

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