Gutter

Manufacturers need to minimise the amount of material used to make their product. What is the best cross-section for a gutter?

Crossing the Bridge

Four friends must cross a bridge. How can they all cross it in just 17 minutes?

Cuboid Challenge

What's the largest volume of box you can make from a square of paper?

The Fastest Cyclist

Age 14 to 16Challenge Level
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?