The great thing about strength training and intervals for fat burning is "efficiency". Because you are working harder, the signal to your body to change is stronger. You cut time when you increase intensity and you burn fat faster.
Now don't worry, I won't be asking you to do hill sprints tomorrow if you aren't exercising today. For a beginner, we just do some slightly faster than normal walking intervals. For intermediate fitness levels, we'll pick up the pace about 20% compared to their normal cardio levels, but again, the work periods are much shorter.
The key is, you must shift to a slightly higher intensity in order to cut time from your workout. But the workout also goes faster, and much more importantly, you will get more results and better fitness from these methods.
It's easy to do these workouts first thing in the AM, at lunch, or after the kids go to bed. Plus, you can get a great workout at home with only a bench, dumbells, and an exercise ball. You don't need fancy machines or an expensive gym membership.
And another bonus, you only need three hard fat burning workouts per week. You don't have to be in the gym six days per week.
On your off days, it's important to stay active for at least 30 minutes, but these days should be unstructured and revolve around being active with your family or hobbies. Don't think of them as workout days, think of them as fat burning, stress reducing activity days.