Here you can see some of our thoughts about this problem:
shows the limitations assuming all other information stays the same when the 7 hour per day limit is relaxed:
This leads to the conclusion that 8 hours per day cycling would give him a very small calorie deficit.
Algebraic solution (where h = hours/day cycling):
Calories available to consume: 4000 + 350h
Calories used: 2500 + (14 x 1.61 x 100h)/4.19
4000 + 350h = 2500 + (14 x 1.61 x 100h)/4.19
h = 7.98 hours per day cycling
If Andy cycles 8 hours per day, total race time:
1407 / (1.61 x 14 x 8) = 7.8 days
= 7 days + 6.422 hours cycling on Day 8
=7 days + 6 hours 25.34 minutes cycling on Day 8
Can you think of any other approaches?