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?

If the speed is s; the two digits a,b
The first number is 10a+b
The second is 10b+a
The third is 100a+b

From the first 2: s = 9b-9a ... Eqn 1
From the second & third: s = 99a-9b ... Eqn 2

Adding: 2s = 90a so s = 45a

Equating eqns 1 & 2
99a-9b = 9b-9a so 108a = 18b i.e. 6a = b
Since a & b are < 10, a=1, b=6

So s = 45

Posted by DrBob on 2003-10-09 17:25:07