Students are going through a three$-$step process to obtain their ID cards. Each student will spend $2$ minutes at the registration desk before going to one of three cashiers to pay a fee for the ID card. After that, he$/$she will visit one of four ID processing stations to have his$/$her picture taken and ID card printed. Visits to the cashier and ID processing station take $10$ and $20$ minutes respectively. If the demand rate is $0\mathrm{.}5$ student per minute, how long does it take to process $20$ students, assuming the system is empty?