Neco Model Questions Vol1 2022 Geography Question 4

Three towns A, B and C form a triangle with side lengths AB = 120 km, BC = 150 km and AC = 180 km. The AB road is paved (average speed 80 km/h) and the BC road is unpaved (average speed 40 km/h). The AC road can be upgraded: paving costs \(500\,000\) Naira per kilometre and allows travel at 80 km/h; the unpaved portion remains at 40 km/h. The government has a budget of \(60\) million Naira for upgrading AC and may pave any length \(x\) (0 ≤ x ≤ 180) kilometres, starting from town A.\n\n(a) What is the maximum length of AC that can be paved within the budget?\n(b) Using that maximum length, calculate the travel time from A to C along the upgraded AC road.\n(c) Compare this time with the travel time via the route A‑B‑C (using the existing roads) and state which route is faster, giving the minimum travel time (rounded to two decimal places).