I just finished the Couch to 5K program last week. I decided to focus primarily on time since I was an absolute beginner. My finishing pace was 4.0mph or 15 minute mile. The most I ran in 30 minutes was 2 miles. I told you I was a beginner

Anyway, I want to be able to run and finish a 5K in less than 40 minutes.
I found a few programs online and many suggest focusing on mileage. For example, the program would have me doing 1.5 miles on Day 1, 1 mile on Day 2 and 1.5 miles on Day 3. Each week the mileage would increase anywhere from a quarter to three-quarters of a mile for each day. I would use 4.0 mph as my base pace and would bump it up on a pretty regular basis. This program lasts for 10 weeks.
Would this type of program help me reach my 5K goal if I am consistently increasing my pace? Is there some way to know when it's time to increase the pace?
Any suggestions would be appreciated.