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The Fastest Cyclist

Age 14 to 16
Challenge Level Yellow starYellow star
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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?


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The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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