A car is travelling at a uniform speed.
The driver sees a milestone showing a 2-digit number. After travelling for an hour the driver sees another milestone with the same digits in reverse order.
After another hour the driver sees another milestone containing the same two digits as in the first one but the two digits separated by a zero(0).
What is the speed of the car?
Assume the first post is AB, then the second is BA, and the third is A0B. Since the drivers speed is constant and the posts are seen at the same interval, the distance between the posts is the same.
So, A0B - BA == BA -AB
That is, 100A + B - 10B - A = 10B + A - 10A -B
or 108A = 18B
or B = 108A / 18
If A = 1, then B = 6.
There are no other solutions where A and B are single digits.
So the posts show 16, 61, and 106.
Howard
Solution
