Hi Linda,
Cycling is excellent exercise and yes, it does incorporate your upper and lower body as well as your core. Be sure to maintain good posture and pull from your abdominal muscles as you pedal - you'll get a great ab workout that way. Obviously, depending on the amount of resistance you are using, the muscles in your legs can also really be challenged and you can help develop some serious lean muscle mass that way.
Because cycling can also be a great aerobic workout, you're burning calories and fat, which is helping to slim your body down everywhere - not just in the aforementioned targeted areas.
Interms of your walking time - good for you! Cutting your time in half is excellent, you've made some terrific progress. Keep challenging yourself to add in those jogs - interval training burns massive amounts of calories and fat.
Keep me posted on your progress, and let me know if I can help any further.
Good Luck,
Paul