I would do both!
Maybe on weekdays you can start a Learn to Run or C25K program to see if you enjoy running vs. walking. These will start you out at a level that's comperable to what you're doing now (you don't *have* to run/jog if you don't want to, of course, but it's a good way to see if you'll like it).
On the weekend (or a day off when you have a little more time), you can work on distance. Walk at a steady, comfortable pace and build your miles. The recommendation is usually about a 10% increase per week on your milage, so you could set a distance goal (3.1 miles / 5k would be a great one to start) and build up to that and beyond.
You'll notice with a lot of training programs they do a combination of different types of runs - slower distance runs to build mileage, faster short runs to build speed, hill runs to tap into higher intensity exercise. Each day has a different purpose, so even though you're doing the same activty, it's really several different workouts. There's no reason you can't do something similar with your walking.
|86 Days until: Calgary Marathon