Well, the Moon goes once around the Earth every 27.2 days at a typical distance of 384,400 kilometers. The circumference of the orbit is just 2 x pi x 384,400 kilometers or 2,414,000 kilometers, and since 27.2 days is 652.8 hours, that works out to about 3697 kilometers/hour.
If you estimate that the Earth's diameter is 2 x 6400 = 12,800 kilometers, and the lunar eclipse takes about 2 hours, you end up with a speed of the Earth's shadow that is about 6,400 kilometers/second. This 2 hour figure is only the typical length of 'totality' and doesn't very well include the time for ingress and egress which, I believe, give a full shadow passage time closer to 4 hours, and so a shadow speed closer to 3700 kilometers/sec. For the April 4th, 1996 eclipse, for example, totality lasted 1 hour 10 minutes, but the entire eclipse lasted from 0:12 to 5:36 UT or 5 hours, 24 minutes.