Problem $18-2($Algo$)$

A vending machine dispenses hot chocolate or coffee. Service time is $45$ seconds per cup and is constant. Customers arrive at a mean rate of $59$ per hour, and this rate is Poisson$-$distributed.

a$.$ Determine the average number of customers waiting in line. $($Round your answer to $2$ decimal places.$)$

b$.$ Determine the average time customers spend in the system. $($Do not round intermediate calculations. Round your answer to $2$ decimal places.$)$