This isn't what the poisson distribution tells you.
You will, on average, wait 10 minutes. If you hitch hiked that road 1000 times, you'll have waited 10 minutes on average.
But that doesn't mean you won't wait longer that 10 minutes on a given wait. In theory, you're waiting time will follow an exponential distribution, so you could wait 1, 10, 50, or even 1000 minutes (although quite unlikely)!
But again... On average, you'll be waiting for 10 minutes from car to car.
You will, on average, wait 10 minutes. If you hitch hiked that road 1000 times, you'll have waited 10 minutes on average.
But that doesn't mean you won't wait longer that 10 minutes on a given wait. In theory, you're waiting time will follow an exponential distribution, so you could wait 1, 10, 50, or even 1000 minutes (although quite unlikely)!
But again... On average, you'll be waiting for 10 minutes from car to car.