A water wave is a shallow-water wave if the water depth d is less than /10.

A water wave is a shallow-water wave if the water depth d is less than ≈ λ/10. It is shown in hydrodynamics that the speed of a shallow-water wave is v = √gd, so waves slow down as they move into shallower water. Ocean waves, with wavelengths of typically 100 m, are shallow-water waves when the water depth is less than ≈ 10 m.
Consider a beach where the depth increases linearly with distance from the shore until reaching a depth of 5.0 m at a distance of 100 m.
How long does it take a wave to move the last 100 m to the shore?
Assume that the waves are so small that they don’t break before reaching the shore.