When I cast my mind back many decades to maths at school - we did such boring examples - like the ladder leaning against the wall and the gravitational forces exerted on it. Not much relation to real life, because when someone wants to lean a ladder, they also take into account the softness, slipperyness etc of the ground and the weight of the Bloke on the ladder. Same as digging that trench. If you calculate how long it will take three men, you are not suddenly going to have twelve men turn up for work are you.
My point is, and there is one,
your topic seems much more relevant to real mathematics in situations.
You have been given lots of good ideas. Would you like some more?
What about the finances involved, and balancing budgets? The budget for a team in the TdeF for a race might be X Euros. There is transport, hotels, food, incidentals, new wheels, not to mention wages. Some of these would be fixed costs of-course, but some negotiable. Plus the prize money going in the "pot". Then if it goes into Switzerland, which some years it does, the costs have to be recalculated into Swiss Francs.
Then there is time management. Loading a team and bikes onto transport takes x hours, and you have to travel x miles/kilometres at an average speed of x, and then setting up takes x long, what time does the team have breakfast?
One of the vehicles breaks down at town A, how long does it take another vehicle to reach it from town B?
