I would just do whatever the distance is, even if it means that your workout session is longer. Good luck!

If you're talking about C25K, then you misunderstand.  It does NOT assume you do 10 minute miles.  The program is to run EITHER 30 minutes OR 3 miles - not necessarily that you run 3 miles in 30 minutes.

The reason they pick that time/distance is simply because it makes easy math and it is an average pace, not because all new runners can run a 10 minute mile. Too many people doing C25K get discouraged because they don't meet that arbitrary pace.  So choose whether your goal is the time or the distance.  If you are a slower runner, then you will probably want to go by time as you will reach the 30 minute goal before you reach the 3 mile goal (which would be 36 minutes at your pace).

Just walk/run the allotted minutes in the program and don't stress about distance for now.  Once you complete the program then you can start working on running faster and longer distances.  Make the program work for you at your fitness level.  One step at a time - you'll get there!

I have done 11 marathons and 40+ half marathons. I do 16 minute miles. Speed doesn't matter. Time for endurance do. Even the month before a marathon, like NYC, I may do about two   3 hour "runs" about 4 weeks out and about 5 miles 4 days a week for 12-14 weeks before. I can't go any faster, but I always finish. Good luck.