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 answer by K Sengupta)

Let the respective values in the three milestones be 10A+B, 10B+A and 100A+ B.

Since the driver drove the car at a constant speed, we must have:

(10B+A) - (10A+B) = (100A +B) - (10B+A)
or, 100A+B + 10A+B = 2(10B+A)
or, 110A+2B = 20B+2A
or, 108A = 18B
or, 6A = B

Since 10A+B is a two digit number, we must have A>=1. If A>=2, then B>=6*2=12>10, which
is a contradiction. This A =1, giving B=6

So the respective values in the three milestones were 16, 61 and 106. Accordingly, the car covered 61-16= 45 miles in one hour, so that  the required speed of the car is 45 miles per hour.      

Posted by K Sengupta on 2008-02-14 13:48:33