All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
There is nothing wrong with leasing these vehicles for a known fee, for a known period, or for a known distance. The fact that the contract is based on usage, not on time, does not affect it as if the contract was such that every specified distance has a specified fare. So, if he travels a distance of a kilometer, his fare is such and such, and if he travels half a kilometer, his fare is such and such. In other words, the fare is based on the distance traveled, so apparently there is nothing wrong with it due to its well-defined regulation and the absence of ignorance in it.
If the intended meaning is something else, kindly provide clarification so that we may offer an accurate answer.
Allah knows best.