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?

(In reply to Puzzle Solution (Method I) by K Sengupta)

It is evident that the first two milestones contain two digits, while the third milestone contain three digits.

Also, by the problem,  the first milestone, second milestone and the third milestone (in this order) describe an arithmetic sequence.

Since both the first milestone (f) and the second milestone (s) 
contain two digits, it follows that the maximum common difference = max(s-f) = 99-10 =89, giving the maximum value in the third milestone as 99+89 = 188<200. Thus,  the first digit of the third milestone, which is equal to the first digit in the first  milestone must be 1.

Thus, the displays on the three milestones are 10+B, 10B+1 and 100+B. Accordingly, the given conditions yield:

10+B + 100+B = 2(10B+1)
or, 18B =108, so that: B=6

Thus, the respective displays on the first milestone, second milestone and the third milestone are 16, 61 and 106.

Hence the car traverses precisely 61-16= 45 miles in each hour, so that the speed of the car is 45 miles per hour.

 

Edited on February 15, 2008, 10:53 am

Posted by K Sengupta on 2008-02-14 13:51:15