A toll tunnel has decided to experiment with the use of a debit card for the collection of tolls. Initially, only one lane will be used. Cars are estimated to arrive at this experimental lane at the rate of $500$ per hour. It will take exactly $5\mathrm{.}0$ seconds to verify the debit card.

How much time would you expect a customer to wait in line, pay with a debit card, and leave?

Note: Round your intermediate calculations to $3$ decimal places and final answer to $1$ decimal place.