Interstate 81 through southwest Virginia is heavily traveled by long-distance truckers. To cut down on accidents, The Virginia State Patrol carries out random inspections of a trucks weight and the condition of its brakes. On Fridays, trucks approach the inspection station at a rate of one every 45 seconds following a Poisson process. The time required to check a truck's weight and brakes follows an exponential distribution with an average inspection time of 5 minutes. The state troopers only pull over trucks when at least one of their three portable inspection units is available.

On average, how many trucks will be pulled over for inspection each hour?

Please show work as to how you got the answer. I believe the answer is 45 trucks.