A man leaves Paris driving at a constant speed After a while

A man leaves Paris driving at a constant speed. After a while he passes a kilometer stone that displays a 2 digit number. An hour later he passes another kilometer stone displaying the same 2 digit number but in reverse order. Another hour after that, he passes a 3rd kilomer stone marker with the same 2 digits(in any order seperated by a zero. What is the speed of the man\'s car?

Solution

two digit x and y
;
Let (10x + y) = 1st km marker
then: (10y + x) = 2nd km marker
and: (100x + y) = 3rd km marker
:
2nd marker - 1st marker = 3rd marker - 2nd marker
(10y + x) - (10x + y) = (100x + y) - (10y + x)
10y + x - 10x - y = 100x + y - 10y - x
9y - 9x = 99x - 9y
Simplify, divide equation by 9
y - x = 11x - y
y + y = 11x + x
2y = 12x
:
In order for y to equal a single digit, x has to = 1
2y = 12
y = 6
:
1st marker = 16
2nd marker = 61
3rd marker = 106
:
106 - 61 = 45 km in one hr therefore speed = 45 km/hr
;
Check:
61 - 16 = 45 km