Tiles $(($:${12}^{\text{'}\text{'}}{12}^{\text{'}\text{'}}\}$ can be installed at a rate of $45$ per worker hour. The floor of a large lobby area $({100}^{\text{'}}$ by $($:${50}^{\text{'}}\}$ is to be covered with these tiles. If five workers are assigned to this task, what duration $($to the nearest whole day$)$ should be assigned this activity? Assume $8$ hour days