Answer:
If 67.5% of the 540 km road between the two cities is paved, then the length of the paved road is:
Length of paved road = 67.5% of 540 km = 0.675 x 540 km = 364.5 km
The length of the unpaved road is the remaining distance:
Length of unpaved road = 540 km - 364.5 km = 175.5 km
Let's call the speed of the car on unpaved roads "x". Then, according to the problem, the speed of the car on paved roads is "x + 25". We can use the formula:
Time = Distance / Speed
to set up two equations based on the paved and unpaved parts of the road. We know that the total time to cover the entire road is 10 hours, so we can use this to solve for the two unknown speeds:
Time on paved road + Time on unpaved road = 10 hours
Length of paved road / (x + 25 km/h) + Length of unpaved road / x km/h = 10 hours
Substituting the values we found earlier, we get:
364.5 km / (x + 25 km/h) + 175.5 km / x km/h = 10 hours
Multiplying both sides by the LCD, we get:
364.5x + 175.5(x + 25) = 10x(x + 25)
Simplifying and solving for x, we get:
540x = 10000
x = 18.52 km/h
Therefore, the speed of the car on unpaved roads is 18.52 km/h, and the speed on paved roads is x + 25 = 43.52 km/h.