Let x be the number of miles the car has to go before the numbers contain the same digits

Let y be the new milometer reading

173.3 + x = y/10 (1)

4631 + x = y (2)

Multiply (1) by 10: 1733 + 10x = y (3)

Equating (2) and (3): 1733 + 10x = 4631 + x

9x = 2898

x = 322

Therefore the car must travel 322 more miles.

The two readings are 4953 and 495.3 . The first is 10 times the second.

The starting numbers have to have a difference which is a multiple of 0.9.