THE ANSWER:
First, Carolyn and Deliah cross the bridge (which takes 2 minutes).
Then, Carolyn crosses back (another 2 minutes).
Andrea and Barbara then cross together (which takes 10 minutes).
Delilah crosses back (which takes 1 minute).
Finally, Carolyn and Delilah cross the bridge once more (which takes 2 minutes), for 17 total minutes.