Dear Kirsten,
Solar storms that are ejected from the Sun travel through space for a long time (many days). When they first get ejected from the solar surface, some of them are traveling extremely fast and it only takes them a few minutes to get far from the Sun. The flares that are associated with solar storms can sometimes only last a few minutes. There is a wide range of times and speeds involved with these storms, but they are very fast compared to the speeds we're used to dealing with here on Earth.
Hope this answers your question!
Holly