Once a couple was caught in an unending argument due to some unknown reasons. They got irritated from each other and decided to move away. They started moving with velocities \(\sqrt{2+\sqrt{2}} \text{ m/s}\) at the same time from the junction of two roads inclined to \(45^{\circ}\) to each other. If they travel by different roads, find the rate at which they are being separated?

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