SOLUTION: 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 displayi

Question 172884: 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?
Found 2 solutions by ankor@dixie-net.com, Mathtut:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
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 kilometer stone marker with the same 2 digits(in any order separated by a zero. What is the speed of the man's car?
:
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
Answer by Mathtut(3670) (Show Source): You can put this solution on YOUR website!
another way to look at this is thru elimination
:
we are given that the 3rd kilometer marker has a zero in between the numbers.
:
so we only have so many numbers to check to see if they fit the rest of the criteria, which is the two numbers that surround the zero are numbers that are reversed at the other two markers and that his speed is constant.
:
102
103
104
105
106
107
108
109
:
so our possible numbers are 12,13,14,15,16,17,18,19 and those numbers reversed
:
21-12=9........102-21=81
31-13=18.......103-31=72
41-14=27.......104-41=63
51-15=36.......105-51=54
.......the only ones that fit
71-17=54.......107-17=36
81-18=63.......108-18=27
91-19=72.......109-91=18
:
so at a steady 45km/hr he passed milestone 16,61,and 106.......took him a little over a 1/3 of an hour to reach the first kilometer stone of 16
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