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 II)
by K Sengupta)
Let the respective displays on the first milestone, the second milestone and the third milestone be 10A+B, 10B+A and 100A +B.
By the problem, the distance traversed by the car in 2 hours is (100A+B) - (10A+B) = 90A, and so the car traverses 45A miles in each hour.
Since the display in the first milestone(f) contain two digits, it follows that f>=10 and accordingly, if A>=2 then the display in the second milestone is >= 10+ 45*2 = 100, which is a three digit number. This leads to a contradiction.
For A=0, the respective displays in the first and the third milestone are equal.This is a contradiction.
Thus, A=1 so that the required speed of the car is 45*1 =45 miles per hour.
( As a verification, since A=1, and the speed of the car is 45 miles per hour and the display on the second milestone is the reverse of the first, it follows that:
(10B+1) -(10+B) = 45
or, B = 45/9 + 1 = 6
Thus, the respective displays on the three milestones are 16, 61 and 106 which conforms to all the conditions of the given problem).