1 & 2- The change is incorrect- we wouldn't use a gerund there.
3 & 4- This changes the meaning and suggests that she got the ticket for speeding as a way of getting to the airport on time, which isn't logical.
These transformations don't really work to me- the gerund and infinitive are not alternate forms, and where both can be used they normally cary a different meaning.
Snowed in = unable to get out because of the snow
for = the length of time
Student or Learner