Calories burned per hour at distance raced
Swimming 4.5km burns 600 kcal per hour = 1.5km burns 200kcal per hour
Cycling 30km burns 900kcal per hour = 40km burns 1200kcal per hour
Running 15km burns 1100kcal per hour = 10km burns 733kcal per hour
Calories burned per minute at distance raced
Swimming - 200kcal per hour = 3kcal per minute
Cycling - 1200kcal per hour = 20 kcal per minute
Running - 733kcal per hour = 12 kcal per minute
Calories burned by Adam
Swimming - 19 x 3 = 57kcal
Cycling - 1200 + (5 x 20) = 1300kcal
Running - 32 x 12 = 384kcal
Total - 1741kcal
Calories burned by Ben
Swimming - 21 x 3 = 63kcal
Cycling - 1200 + (5 x 20) = 1300kcal
Running - 32 x 12 = 384kcal
Total - 1747kcal
Calories burned by Charles
Swimming - 23 x 3 = 69kcal
Cycling - 1200 + (3 x 20) = 1260kcal
Running - 30 x 12 = 360kcal
Total - 1689kcal
Conclusion
Ben burns the most calories.
I am not surprised because Ben took the most time overall and the most time in the cycling, which burned the most calories per hour.
The modelling assumptions are not valid because the actual rate of calories burned is not directly proportional to speed and different people burn calories at different rates.