Go the Distance with Careetone

To simplify the problem, we can scale down the number of kilometers the front and back wheels can go by a factor of } $1600$ , leaving us with the the rear tires being able to go $21$ kilometers and the front tires being able to go $29$ kilometers. Now suppose you go $x$ kilometers, the front tires will wear down by $\frac{x}{21}$ while the back tires will wear down by $\frac{x}{29}$ .
The total amount of wear will be $2 \times \frac{x}{21} + 2 \times \frac{x}{29} = \frac{100x}{609}$ . Maximum distance occurs when we evenly distribute the amount of wear between all 5 tires. The number of kilometers that can be covered by the tires is: $5 \times \frac{609}{100x } \times x = \frac{609}{20}$ . Scaling that back up by the factor of 1600, we get the final answer to be: $\frac{609}{20} \times 1600= \boxed{48720 kilometers}$ .