This spreadsheet shows the limitations assuming all other information stays the same when the 7 hour per day limit is relaxed:
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
Calculations below relate to Yanqing's original version of the problem.
Cycling calories = 3750 a day, so total 6250 calories a day. (rounded)
Meals 3000
3250 remaining to be made up from:
Off-road snacks up to 1000
On-road snacks up to 2450.
Gives an extra 200.
Bananas 120, 12kcal for 1p, 1kcal for 1g, holds 8
Cereal bar 100, 6.25kcal for 1p, 4kcal for 1g, holds 16
Gel 110, 1.1 kcal for 1p, 2.6kcal for 1g, holds 24
energy bar 220, 2.2kcal for 1p, 3.4kcal for 1g, holds 8
drink 190, 1.3 kcal for 1p, holds 6.
Possible plans:
Meals, full off-road snacks, 8 energy bars, 2 (and a bit) servings of drink
Meals, 24 packets of gel, 850 kcal of snacks
Meals, 16 cereal bars, 3 (and a bit) servings of drink, full snacks
For cheapest and lightest, sensible to maximise off-road snacks.
Cheap: 16 cereal bars, 3 and a bit servings of drink costs about £7.30 a day.
Light: topping up water the full 4 times, start with 1 bottle (2 servings) of energy drink, then 8 energy bars.
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Going for 7.85 hours for 8 days requires 2700kcal on the road per day, doable but must use lots of gel.
Now going for 9 hours for 7 days:
7300 kcal a day, so 3300 for on the road! That's over the limit for energy absorption, so he will need to eat more off the road.