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 solution by Freddy Grants)

In one hour, the driver travels ba-ab miles with the speed v : v*1=ba-ab <=> v*1=10*b+a-10*a-b <=> v=9*b-9*a (1) ;
Then after another hour, the driver travels a0b-ba miles with the same speed v: v*1=aob-ba <=> v=100*a+b-10*b-a <=> v=99*a-9*b (2);
In total, in 2 hours, the driver travels a0b-ab miles with the same speed v: a0b-ab=v*2 <=> 2*v= 100*a+b-10*a-b <=>v=45*a => a=v/45 (3) ;
In 9*b-9*a=v (1) we have a=v/45 (3) =>b=(6*v)/45=6*a
So, a=v/45 and b=6*a; We know that a and b are numbers from 1 to 9 so, the only posibility is a=1 and b=6 (for a>1 => b>10 which is not possible); a=v/45=1 => v=45 miles/hour;

Posted by Ruxi on 2003-10-06 15:00:05