The odometer shows a palindromic number, a number that is the same written forwards and backwards. Two hours later the number is palindromic again. How fast was the car going, if the first number was 15,951 miles?

That would be 16,061.

Let's suppose you travel at 60 mph. In one hour, you would have traveled 60 miles ... and in two hours 120 miles.

Let's add the 120 to 15,951. That would be 16,071 miles traveled. I see that there * IS * a palindromic number very close to that number: 16,061.

Boo Yah!