A rectangular cooler holding crushed ice and water is comprised of a $2$ mm polypropylene internal wall and a $1$mm stainless steel $($AISI $316)$ outer shell, with $5\mathrm{.}5$ cm of expanded polystyrene foam between them. If the cooler measures $0\mathrm{.}75$ m x $0\mathrm{.}25$m x $0\mathrm{.}5$m$,$ and is filled with a $50-50$ mixture of ice and water, if it is sitting, with its lid $*$closed$*$ in a room that is $35\backslash$deg C with a heat transfer coefficient of $30$ W$$m$-1$K$-1,$ how long will it take for all of the ice to melt? Assume that the air and the floor of the room are the same temperature, and the base of the cooler shares the same materials as the walls, and ignore corner effects for conduction. The picture shows dimensions, but to reiterate, the lid is closed.