Formula None Racer!

Let the two digit number be represented by $10x+y$ .

After one hour, the milestone shows the number $10y+x$ .

The distance traveled so far is: $(10y+x) - (10x+y) = 9(y - x)$

After another hour, the milestone shows $100x+y$ .

The distance traveled in the second hour is: $(100x+y) - (10y+x) = 9(11x - y)$ .

Since the speed is uniform, we have: $9(11x - y) = 9(y - x)$

This gives $y = 6x$ . Since $x$ and $y$ are both digits, $x$ must be $1$ and $y$ must be $6$ .

Therefore, the milestones mentioned read: $16$ , $61$ and $106$ .

Now, since the car traveled $45$ miles each hour, it is clear that the speed of the car is $45$ mph.