What is a tsunami?
Tsunamis are giant waves caused by earthquakes or volcanic eruptions under the ocean. When tsunami waves travel inland, they get larger as the depth of the ocean decreases. If you know your fluid dynamics you know why the speed of tsunami waves varies with ocean depth rather than the distance from the earthquake.
How fast? As fast as an airplane in some cases, slowing down only in shallow waters. The largest tsunami was also in Japan, Ishigaki Island in 1971. It was 278 feet high (that is a 30-story building) and carried a 750-ton block of coral 1.5 miles inland.