Question 172906: Tim leaves Paris, driving at a constant speed. After awhile he passes a milestone displaying a two-digit number. An hour later he passes a milestone displaying the same two-digit number but in reverse order. In another hour, he passes a third milestone with the same two-digits (backwards or forwards) seperated by a zero.
What is the speed of Tim's car?
Answer by Mathtut(3670)   (Show Source):
You can put this solution on YOUR website! we are given that the 3rd kilometer marker has a zero in between the numbers.
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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.
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102
103
104
105
106
107
108
109
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so our possible numbers are 12,13,14,15,16,17,18,19 and those numbers reversed
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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
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remembering that speed is constant means that the difference between hour 2 and 1 must equal the difference between hour 3 and 2. the only place this happens is at 16,61,and 106
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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 milestone of 16
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