In what time period? Blue whales exist in every ocean, and it is possible, though unlikely, that some individuals have circumnavigated the globe. As their average speed is approximately 12 kilometers per hour, one imagines they travel approximately 100 kilometers/day.
http://en.wikipedia.org/wiki/Blue_Whale
It varies by species, but on average, a whale can swim anywhere from 50-100 miles daily. Some species, like the humpback whale, may travel even greater distances during migration.
in the ocean
swim
PEOPLE!
they swim.
Yes. Many, many miles. Typically whales migrate each season from cold water either near the Arctic or Antarctic (not all whales swim the same route) then back to the warmer waters maybe near the equator. Just look up whale migration routes and you will find plenty of maps to look at, or you could search for a specific whale and its migration patterns.
cold
A Humpback Whale can swim up to 17 miles per a hour!
As far as a blue whale can swim in a year
10000km
The Blue Whale can swim at an amazing speed of 30mphThe blue whale swims so fast that biologist have to resort to aircraft to watch them. They are too fast for boats. (Probably not too fast for warships but the military isn't going to waste their time watching whales.)
Between 10,000 and 25,000 blue whales are believed to still swim the world's oceans.