Five tyres over $40000$ kilometres

Question

The five tyres of a car (four road tyres and one spare) were used equally in a journey of $40,000~\text{km}$. The number of kilometres of use of each tyre was

a. $40000$
b. $10000$
c. $32000$
d. $8000$

This is what I tried. I just want to know is my approach is correct or not. Or is there any better method to solve this type of question?

Total kilometers travelled by $4$ tyres $= 40000 \cdot 4 = 160,000$.
This has to be shared by $5$ tyres.
So each tyre capacity $= \frac{160,000}{5} = 32,000$.
After we travel $32,000~\text{km}$, we are left with $4$ worn tyres and one new tyre. But if the tyres are rotated properly after each $8000~\text{km}$,

Answer 1

You will switch tires $4$ times so every tire has a chance to run. So you will be making $5$ lags, and so each lag will be $8000$. So each of the $5$ tires rests in a lag of $8000$. Or, each tire runs a total of $32000$

Answer 2

You have to consider that every tire, in order to have equal use, had to at least once have been in the spare tire compartment. This means that there were 5 journeys in between the tire changes. Each journey was 8000km long (40,000/5). So, because each tire was on the road per journey segment except for 1, each tire was used a total of 32,000 times (8000x4)