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The Fastest Cyclist

Age 14 to 16 Challenge Level:
Here you can see some of our thoughts about this problem:
This spreadsheet
 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?