#### Answer

The closest distance that another swimmer could be so that the motion is exactly the opposite is 4.8 meters.

#### Work Step by Step

The waves have a wavelength of 9.6 meters. If another swimmer is 9.6 meters away along the direction of motion of the waves, then the two swimmers will bob up and down at the same time.
If a third swimmer is exactly in the middle of these two swimmers, then this swimmer will bob and down with the exact opposite motion. Note that this opposite motion occurs when the swimmer is a distance of half a wavelength away along the direction of motion of the waves.
The closest distance that another swimmer could be so that the motion is exactly the opposite is 4.8 meters.