Yep, that's a great idea. If you can run it all, then GFI, but if it's pushing you, then it's better to approach it that way.
When I first started running, the advice given to me was to think in terms of time on feet rather than miles because that's where you start to build up your endurance. I was advised to start 3 x 30 mins, then move on to 3 x 40 mins, 50 mins etc. I had a number of injuries before running (through years of playing netball) so had to take it easy which was another reason for a slower buildup. Sometimes I used to add the extra 10mins at the end of my run by doing a run / walk combo as I didn't want to push the injured bits (feet, ankles and knees).
I also think that it's better to keep moving in a regular way, ie run/walk, than running until you drop, then having to walk the rest because you're knackered.
I got to 3 x 60mins, then added in an extra day and gradually built it up to being able to run 6 days (45 - 50m) every week. I do HR training, where the emphasis is on slower, controlled miles, but I've managed it without injury and at the ripe old age of 50+.
Sorry, have to go, but keep asking questions if it helps.