How fast can dolphins swim? Very fast, as fast as the fastest boats. What's their average cruising speed? According to [1] it's about 8 km/h. They do sleep and when they sleep they don't move much. It is difficult to track dolphin travel over long periods of time but lately there's been some progress it seems. Check out this graphical view ("Track the dolphins") of three dolphins around Bermuda. Even with tracking the crew reported difficulty in actually finding the animals with their boat.

Day 3 Satellite transmission received from Ace Boy at 7:00 am placing him near the south west of Bermuda. The next transmission told us he was headed north east around Bermuda. We tried to catch up with him but we could not find him.

[1] Rohr, J. J. et al. Observations of Dolphin Swimming Speed and Strouhal Number. Space and Naval Warfare Systems Center Technical Report No. 1769 (Space and Naval Warfare Systems Center, San Diego, 1998)