How do people use math by building roads?

Answer 1

Measure traffic flows and predict future flows to decide whether or not a road is required. Cost-benefit analyses to decide whether it should be built, and whether it should be one-lane, two-lane or more.

Determine the best route taking account of the length of each stretch against the cost of building it over terrain that will change. A bridge may be more expensive on a per-mile basis, but the alternative may be a very long detour. Decide on the gradient of the road so that vehicles can climb up or down safely.

Decide on amounts of raw materials, manpower, machinery required. Critical path analyses to decide what tasks must be done in what order. Plan and arrange financing. And all that is before the first machine moves in.