Alice leaves Denver driving at a constant speed After a whil

Alice leaves Denver, driving at a constant speed. After a while, she passes a mile marker displaying a two-digit number. One hour later, she passes a second marker with the same two digits in reverse order. In another hour she passes a third marker with the same two numbers separated by a zero. What is the rate of Alice\'s car in miles per hour?

Solution

If we find the value of the mile markers we can find the speed easily.
:
Let the 1st number be:
10x + y:
then
10y + x = the second number
and
100x + y = the third number
:
We know:
3rd marker - 2nd marker = 2nd marker - 1st marker
(100x + y) - (10y + x) = (10y + x) - (10x + y)
:
100x + y - 10y - x = 10y + x - 10x - y
:
99x - 9y = 9y - 9x
:
11x - y = y - x; simplified, divided by 9
:
11x + x = y + y
:
12x = 2y
or
6x = y
:
In order for y to be a single digit, x = 1.
:
1st mile marker = 16
2nd mile marker = 61
3rd mile marker = 106
:
The difference between the markers is 45 miles, therefore her speed = 45 mph