The top rates of fat oxidation (fat burning) are around 1.5 g/min at high intensity levels. At that level an hour would burn 90g of fat or 810 calories. Marathon runners are said to expend about 1,000 calories an hour but that might be largely carbohydrates (around 75%).
Lightly active fat oxidation rates are 31 g/lb of fat mass per day (Hypophagia – How much fat can I lose in a day?). Assuming a 170 lb person with 10% body fat that’s 17 lbs times 31g/lb = 527 cals a day. At that body fat it would take a week to lose a lb. This also means that the diet can’t be at a larger caloric deficit than that amount (exercise as above is the exception).
Assuming that the 170 lb person expends about 12 calories per lb of body weight that’s a daily caloric expenditure of 2040 calories. Cutting calories for a caloric deficit to around 1500 would result in maximum fat loss.
But this is only true if the person gets enough protein. Ideally, that would be around 0.8 g per lb of lean body mass for a lightly active person. This person would need to eat 136g of protein a day.
Eating the protein in four meals of at least 30 grams of protein would spare the most muscle mass while rapidly losing weight.
Macros would then be:
- 136 g protein
- 20 g carbs
- 97 g fat
It might be tempting to drop fat or protein but that would be a mistake since it would not result in larger losses.
Combine that with intense activity (as noted) a greater weight of loss can be achieve.
I have a calculator for this at Keto Calculator.