Andy is cycling from Land's End to John O' Groats.
Distance: 1407 km
Speed: 14 mph*1.61=22.86 kph
We now know Andy's speed; 22.86 kph (I will be using kilometers for this question).
NUTRITION
Andy, as a grown man, needs 2500 kcal per day, plus 100 kJ (* 4.19= approx. 24 kcal).
Andy eats 3 Really Big Meals a day on trips that take more than one day, which all contain 1000 kcal (kilo calories).
1000*3= 3000 kcal
He can also have snacks, which are the following, with nutritional values:
Bananas (b): 120kcal, 10p, 120g
Energy Gel (eg): 110kcal, £1, 42g
Energy Drink, 500ml (ed): 190kcal, £1.39, 500ml
Energy Bar (eb): 220kcal, £1, 65g
Cereal Bar (c): 100kcal, 16p, 25g
Andy and his bike only have 3 1L bottle holders, and 8 pockets in his jersey which each hold 1b, 1eb, 3eg, or 2c. This means that his maximum energy intake per day is as follows;
3 energy gels per pocket
3*8=24
24*110kcal=2640kcal
That means that Andy can have 5640 kcal from food per day. He can only have 1000 kcal of snacks off road, meaning the remainder will have to be in meals or on the road.
Now, Andy can also have energy drinks. He can carry 3 1L bottles, which means that he can carry 6 portions of energy drink.
190 kcal*6=1140 kcal
This collectively means that Andy can consume 6780 kcal of energy in one day.
TIME
A normal grown man needs 2500 kcal a day. This means we must subtract this from Andy's daily intake on this trip. Andy also needs 100 kJ to cycle 1 km.
1kcal=4.19 kJ
6780kcal-2500kcal=4280 kcal
4280kcal*4.19=17933.2 kJ
17933.2 kJ/100 kJ=179.332
This means that Andy can cycle 179.332 km in one day. Earlier, we found out that the distance from Land's End to John O' Groats is 1407 km.
1407 km/ 179.332 km= approx 7.85
So it would take Andy 7.85 days to cycle from Land's End to John O' Groats, which is just under 8 days.