Question

A palindromic number is a number whose digits read the same left to right as right to left. for​ example, 383,​ 12,321, and​ 9,876,789 are palindromic. the odometer of the family car read​ 15,951 when the driver noticed that the number was palindromic.​ "curious," said the driver to herself.​ "it will be a long time before that happens​ again." but 2 hours​ later, the odometer showed a new palindromic number. assuming it was the next possible​ one, how fast was the car driving in those 2​ hours?

Answer 1

The driver was going 55 mph.

Two hours is not enough to change the first digit of 15951, therefore, 1 is the first and last digit of the new number. The fourth and second digits converted to 6 and the middle digit could either by 0, 1, 2, 3, …,9. Therefore, the driven miles will be 110, 210, 310, … respectively.

So in two hours, the car would have sped up at 55 mph, 105 mph, 155 mph, … respectively.